8: Professional Emails
- Identify content appropriate for professional emails.
- Demonstrate how audience influences email content.
- Exemplify the important components of professional emails.
- Explain ethical dilemmas posed by electronic communication.
Writing Effective Professional Emails
Technical writers send emails for internal and external communication purposes. Emails can be brief or lengthy and are quite malleable. Emails are useful tools for messages that are longer than a memo and to conduct business outside the organization. Many businesses send automated emails for regular communication, such to disseminate monthly reports. Many companies have synchronous chat networks so colleagues can exchange information quickly and easily, especially among small groups and teams.
E-mail often serves to exchange information within organizations. Although e-mail may have an informal feel, remember that when used for business, it needs to convey professionalism and respect. As a general rule, writers should never write or send anything they wouldn’t want read in public or in front of the company president.
Ask the following questions to determine if an email is appropriate:
- Is your message long, emotionally-charged, or does it contain highly-confidential information? If so, it may be more appropriate to communicate via a letter, a phone call, or a face-to-face meeting.
- How many emails does the recipient receive each day and what will make them read (or delete) your message?
- Will your recipient deem your email message important, an annoyance, or a waste of time?
- Does the formality and style of your writing fit the expectations of your audience?
- How will your message appear when it reaches the receiver? Is it easy-to-read? Have you used correct grammar and punctuation?
- Did you divide your thoughts into discrete paragraphs and highlight important items, such as due dates, in the text?
- Did you provide enough context for your audience to easily understand and follow the thread of your message?
- Did you identify yourself and make it easy for the reader to respond appropriately?
- Will the receiver be able to open and read any attachments?
Deciding whether it is appropriate to send an email requires you to consider your rhetorical situation. If you recall from earlier in the text, your rhetorical situation refers to your purpose for writing a document and the audience who will receive the message. The questions above offer practical strategies for analyzing your rhetorical situation.
Keep in mind that technical writing is a general term to refer to many different types of documents. As you continue working through this text, remind yourself of the conventions for each type of document. How does a memo differ from an email? When should each be used? What about a letter? Why choose an email rather than a letter? Or vice versa? Again, understanding your rhetorical situation will help you make appropriate decisions about the types of documents to choose. Here are some additional thoughts to help you.
- You need to get in touch with a person who is hard to reach via telephone, does not come to campus regularly, or is not located in the same part of the country or world (for instance, someone who lives in a different time zone).
- The information you want to share is not time-sensitive. The act of sending an e-mail is instantaneous, but that does not mean the writer can expect an instantaneous response. For many people, keeping up with their e-mail correspondence is a part of their job, and they only do it during regular business hours. Unless your reader has promised otherwise, assume that it may take a few days for him/her to respond to your message.

- You need to distribute information to a large number of people quickly (for example, a memo that needs to be sent to the entire office staff).
- You need a written record of the communication. Saving important e-mails can be helpful if you need to refer back to what someone said in an earlier message, provide some kind of proof (for example, proof that you have paid for a service or product), or review the content of an important meeting, deadline, memo.
- Your message is long and complicated or requires additional discussion that would best be accomplished face-to-face. For example, if you want feedback from your supervisor on your work or if you are asking your professor a question that requires more than a yes/no answer or simple explanation, you should schedule a meeting instead.
- Information is highly confidential. E-mail is NEVER private! Keep in mind that your message could be forwarded on to other people without your knowledge. A backup copy of your e-mail is always stored on a server where it can be easily retrieved by interested parties, even when you have deleted the message and think it is gone forever.
- Your message is emotionally charged or the tone of the message could be easily misconstrued. If you would hesitate to say something to someone’s face, do not write it in an e-mail.
As you can see from the complexity noted above, although email is a valuable communication tool, its widespread use in academic and business settings has introduced some new challenges for writers.
Because it is a relatively new form of communication, basic social conventions for writing and responding to e-mail are still being worked out. Miscommunication can easily occur when people have different expectations about the emails that they send and receive. In addition, e-mail is used for many different purposes, including contacting friends, communicating with professors and supervisors, requesting information, and applying for jobs, internships, and scholarships. Depending on your purposes, the messages you send will differ in their formality, intended audience, and desired outcome. Finally, the use of e-mail for advertising purposes has clogged communication channels, preventing some e-mails from reaching their intended audience. Writers are challenged to make their e-mail stand apart from “spam” and to grab and hold the attention of their audience.
So—how do you know when sending an e-mail is the most effective way of getting your message across? When is a brief message o.k., and when it is more appropriate to send a longer, more professional-sounding e-mail? How should a writer decide what style of writing is appropriate for each task? How can you prevent your e-mail from ending up in the junk pile? Keep reading for answers to these questions!
Rhetorical Situation: Who is your audience?
People have different opinions about the form and content of emails, so it is always helpful to be aware of the expectations of your audience. For example, some people regard email as a rapid and informal form of communication—a way to say “hello” or to ask a quick question. However, others view email as simply a more convenient way to transmit a formal letter. Such people may consider an informal e-mail rude or unprofessional.
 Can U help me?
~M
Although it may be obvious to you that you should not send such an email to your professor, let us carefully examine what assumptions this message makes about the reader and his/her expectations.
The tone of this message is very casual; it assumes that the reader knows who the sender is and has a close personal relationship with the sender. Because it contains an ambiguous reference to “the assignment,” this message also assumes that the reader is familiar with the subject matter at hand (for instance, it assumes the reader will know which course and which particular assignment the sender is referring to). In this message, the writer also makes an implicit assumption about the reader’s familiarity with the slang that is often used when sending an instant message or text message. If the reader is not familiar with this type of slang, the “U” in “Can U help me?” might be confusing, or it might even be taken as a sign that the writer is too lazy to type out the word “you.”
Making assumptions about your audience’s expectations increases the risk that your message or its tone will be misinterpreted. To ensure that your message has its intended effect, use the following questions to help you think about your audience and their needs:
- Who is your audience? How often does your audience use e-mail to communicate? How comfortable is your audience with using electronic communication—for example, when in their lifetime did they begin using e-mail (childhood or adulthood)?
- What is your audience’s relationship to you—for example, is the reader your teacher? Your boss? A friend? A stranger? How well do you know him/her? How would you talk to him/her in a social situation?
- What do you want your audience to think or assume about you? What kind of impression do you want to make?
Important Components of an Effective E-mail:
Subject Lines
E-mail subject lines are like newspaper headlines. They should convey the main point of your e-mail or the idea that you want the reader to take away from your e-mail. Therefore, be as specific as possible. One word subjects such as “Hi,” “Question,” or “FYI” are not informative and don’t give the reader an idea of how important your message is. If your message is time-sensitive, you might want to include a date in your subject line, for example, “Meeting on Thurs, Dec 2.”
Greetings and Sign-offs
Use some kind of greeting and some kind of sign-off. Don’t just start with your text, and don’t stop at the end without a polite signature. If you don’t know the person well, you may be confused about how to address him/her (“What do I call my TA/professor?”) or how to sign off (From? Sincerely?). Nonetheless, it is always better to make some kind of effort. When in doubt, address someone more formally to avoid offending them. Some common ways to address your reader are:
Dear Professor Smith,
Hello Ms. McMahon,
Hi Mary Jane,
If you don’t know the name of the person you are addressing, or if the e-mail addresses a diverse group, try something generic, yet polite:
Dear Members of the Selection Committee,
Hello everyone,
Your ending is extremely important because it lets the reader know who is contacting them. Always sign off with your name at the end of your e-mail. If you don’t know the reader well, you might also consider including your title and the organization you belong to; for example:
Mary Watkins
Senior Research Associate
Bain and Company
Joseph Smith
UNC-CH, Class of 2009
For your closing, something brief but friendly, or perhaps just your name, will do for most correspondence:
Thank you,
Best wishes,
See you tomorrow,
Regards,
For a very formal message, such as a job application, use the kind of closing that you might see in a business letter:
Sincerely,
Respectfully yours,
Cc: and Bcc: (‘carbon copy’ and ‘blind carbon copy’)
Copying individuals on an e-mail is a good way to send your message to the main recipient while also sending someone else a copy at the same time. This can be useful if you want to convey the same exact message to more than one person. In professional settings, copying someone else on an e-mail can help get things done, especially if the person receiving the copy is in a supervisory role. For example, copying your boss on an email to a non-responsive co-worker might prompt the co-worker to respond. Be aware, however, that when you send a message to more than one address using the Cc: field, both the original recipient and all the recipients of the carbon copies can see all the e-mail addresses in the To: and Cc: fields. Each person who receives the message will be able to see the addresses of everyone else who received it.
Blind copying e-mails to a group of people can be useful when you don’t want everyone on the list to have each other’s email addresses. The only recipient address that will be visible to all recipients is the one in the To: field. If you don’t want any of the recipients to see the e-mail addresses in the list, you can put your own address in the To: field and use Bcc: exclusively to address your message to others. However, do not assume that blind copying will always keep recipients from knowing who else was copied—someone who is blind copied may hit “reply all” and send a reply to everyone, revealing that he/she was included in the original message.
Additional tips for writing effective emails:
Think about your message before you write it. Don’t send emails in haste. First, decide on the purpose of your e-mail and what outcome you expect from your communication. Then think about your message’s audience and what he/she/they may need in order for your message to have the intended result. You will also improve the clarity of your message if you organize your thoughts before you start writing. Jot down some notes about what information you need to convey, what questions you have, etc., then organize your thoughts in a logical sequence. You can try brainstorming techniques like mapping, listing, or outlining to help you organize your thoughts.
Reflect on the tone of your message. When you are communicating via e-mail, your words are not supported by gestures, voice inflections, or other cues, so it may be easier for someone to misread your tone. For example, sarcasm and jokes are often misinterpreted in e-mails and may offend your audience. Similarly, be careful about how you address your reader. For instance, beginning an e-mail to your professor or TA with “Hey!” might be perceived as being rude or presumptuous (as in, “Hey you!”). If you’re unsure about how your e-mail might be received, you might try reading it out loud to a friend to test its tone.
Strive for clarity and brevity in your writing. Have you ever sent an email that caused confusion and took at least one more communication to straighten out? Miscommunication can occur if an e-mail is unclear, disorganized, or just too long and complex for readers to easily follow.
Here are some steps you can take to ensure that your message is understood:
- Briefly state your purpose for writing the email in the very beginning of your message.
- Be sure to provide the reader with a context for your message. If you’re asking a question, cut and paste any relevant text (for example, computer error messages, assignment prompts you don’t understand, part of a previous e-mail message, etc.) into the e-mail so that the reader has some frame of reference for your question. When replying to someone else’s e-mail, it can often be helpful to either include or restate the sender’s message.
- Use paragraphs to separate thoughts (or consider writing separate e-mails if you have many unrelated points or questions).
- Finally, state the desired outcome at the end of your message. If you’re requesting a response, let the reader know what type of response you require (for example, an e-mail reply, possible times for a meeting, a recommendation letter, etc.) If you’re requesting something that has a due date, be sure to highlight that due date in a prominent position in your e-mail. Ending your e-mail with the next step can be really useful, especially in work settings (for example, you might write “I will follow this e-mail up with a phone call to you in the next day or so” or “Let’s plan to further discuss this at the meeting on Wednesday”).
Format your message so that it is easy to read. Use white space to visually separate paragraphs into separate blocks of text. Bullet important details so that they are easy to pick out. Use boldface type or capital letters to highlight critical information, such as due dates. (But do not type your entire message in capital letters or boldface—your reader may perceive this as “shouting” and won’t be able to tell which parts of the message are especially important.)
Re-read messages before you send them. Use proper grammar, spelling, capitalization, and punctuation. If your email program supports it, use spelling and grammar checkers. Try reading your message out loud to help you catch any grammar mistakes or awkward phrasing that you might otherwise miss.
Sample emails:
Use what you’ve just learned to explain why Student 2’s e-mail to Professor Jones is more effective than the e-mail written by Student 1. How does the tone of the messages differ? What makes Student 2’s e-mail look and sound more appropriate? What are the elements that contribute its clarity? If you were Professor Jones and you received both emails, how would you respond to each one?
hey,
i need help on my paper can i come by your office tomorrow
thx
Hi Dr. Jones,
I am in your ENGL 101 class on Thursdays, and I have a question about the paper that is due next Tuesday. I’m not sure that I understand what is meant by the following sentence in the prompt: “Write a 10 page paper arguing for or against requiring ENGL 101 for all UNC freshmen and provide adequate support for your point of view.”
I am not sure what you would consider “adequate” support. Would using 3 sources be o.k.?
Can I come by your office tomorrow at 2:00 pm to talk to you about my question? Please let me know if that fits your schedule. If not, I could also come by on Friday after 1:00.
Thank you,
Tim Smith
Here are two versions of an e-mail from a supervisor, Jane Doe, to a group of her employees. Which version do you think is most effective? Why?
Subject: tomorrow
As you know, tomorrow afternoon we’ll be meeting to discuss the status of all of our current projects. Donuts will be provided. Be sure to arrive on time and bring along the materials you have been working on this week—bring enough copies for everyone. Some of these materials might include your calendars, reports, and any important emails you have sent. Also, I wanted to remind you that your parking permit requests are due later this week; you should turn those in to Ms. Jones, and if she is not at her desk when you stop by, you can email them to her.
Subject: Materials for Wed. Staff Meeting
Hi, everyone—
For tomorrow’s 3 p.m. staff meeting in the conference room, please bring 15 copies of the following materials:
- Your project calendar
- A one-page report describing your progress so far
- A list of goals for the next month
- Copies of any progress report messages you have sent to clients this past month
See you tomorrow—
Jane
Ethical dilemmas posed by electronic communication
Since emails can contain a lot of personal data, you should take steps to protect your privacy and that of your email recipients. For example, you might use encryption software, or an email server that encrypts your email between your computer and the server, to prevent your personal data from being distributed to the general public. However, the server (and government agencies) can access your data without your knowledge via the server's encryption key. To combat this, Andy Yen recommends you create your own encryption keys, so you own the data and access to the content.
Your employer may require you to sign a confidentiality agreement, in addition to following their code of conduct or ethics. Confidentiality is a safeguard that protects you and your employer from betraying the trust of your readers, clients, colleagues, and supervisors. For example, confidential messages could include proprietary knowledge your organization owns, the financial data of a client, or your own medical or personnel records.
You are ethically and contractually obligated to protect this data when you create internal reports and external promotional materials. For ethical reasons, during written and oral presentations, you should relay all information (positive and negative) to present an accurate picture of the subject. You should never intentionally mislead your audience, even if the purpose is to persuade them to buy a product, or support a policy or procedure change.
Keeping accurate records will help protect you and your organization against questions about confidentiality and other ethical breaches. The rules and regulations vary by industry and individual company policies. For example, many private and public offices have certain legal requirements for electronic record keeping. This "paper trail" can protect your interests and document customer service issues.
- Proper salutations should demonstrate respect and avoid mix-ups in case a message is accidentally sent to the wrong recipient. For example, use a salutation like “Dear Ms. X” (external) or “Hi Barry” (internal).
- Subject lines should be clear, brief, and specific. This helps the recipient understand the essence of the message. For example, “Proposal attached” or “Your question of 10/25.”
- Close with a signature. Identify yourself by creating a signature block that automatically contains your name and business contact information.
- Avoid abbreviations. An e-mail is not a text message, and the audience may not find your wit cause to ROTFLOL (roll on the floor laughing out loud).
- Be brief. Omit unnecessary words.
- Use a good format. Include line breaks between sentences or divide your message into brief paragraphs for ease of reading. A good e-mail should get to the point and conclude in three small paragraphs or less.
- Reread, revise, and review. Catch and correct spelling and grammar mistakes before you press “send.” It will take more time and effort to undo the problems caused by a hasty, poorly written e-mail than to get it right the first time.
- Reply promptly. Watch out for an emotional response—never reply in anger—but make a habit of replying to all emails within twenty-four hours, even if only to say that you will provide the requested information in forty-eight or seventy-two hours.
- Use “Reply All” sparingly. Do not send your reply to everyone who received the initial e-mail unless your message absolutely needs to be read by the entire group.
- Avoid using all caps. Capital letters are used on the Internet to communicate emotion or yelling and are considered rude.
- Test links. If you include a link, test it to make sure it is complete.
- E-mail ahead of time if you are going to attach large files (audio and visual files are often quite large) to prevent exceeding the recipient’s mailbox limit or triggering the spam filter.
- Give feedback or follow up. If you don’t get a response in twenty-four hours, e-mail or call. Spam filters may have intercepted your message, so your recipient may never have received it.
This work "Writing Effective Professional Emails" is a derivative of " ENGL210 Study Guide " and " Unit 2: Internal Communication " by Saylor Academy and " ENGL145: Technical and Report Writing " by Amber Kinonen, used under a CC BY license. "Professional Emails" is licensed under CC BY 4.0 by Tamara Girardi .


29.1: Voice Leading Secondary Chords
29.1 Voice Leading Secondary Chords
When voice leading secondary chords, one largely follows voice leading rules for seventh chords:
-
Resolve the 7th of a chord down by step.
-
Alternate complete voicings with incomplete voicings when voice leading
successive root position seventh chords
. Note that with secondary chords, the 3rd of the chord, typically a raised note, will resolve down by half step to the 7th of the next chord, which is a diatonic note that cancels out the chromaticism of the previous note.
-
Follow the
principle
for resolving viivii∘7 and vii
ø
viiø7 when dealing with secondary viivii∘7 and vii
ø
viiø7 chords.
-
An important exception occurs when viiVvii∘7/V or vii
ø
Vviiø7/V resolves to V. If the melody requires the 7th of the chord to be voiced above the 3rd of the chord, solve the example by writing parallel (unequal) fifths instead of the doubling of the leading tone, which is considered less acceptable.
-
An important exception occurs when viiVvii∘7/V or vii
ø
Vviiø7/V resolves to V. If the melody requires the 7th of the chord to be voiced above the 3rd of the chord, solve the example by writing parallel (unequal) fifths instead of the doubling of the leading tone, which is considered less acceptable.


34.6: High-temperature Superconductors
Learning Objectives
By the end of this section, you will be able to:
- Identify superconductors and their uses.
- Discuss the need for a high-T c superconductor.
Superconductors are materials with a resistivity of zero. They are familiar to the general public because of their practical applications and have been mentioned at a number of points in the text. Because the resistance of a piece of superconductor is zero, there are no heat losses for currents through them; they are used in magnets needing high currents, such as in MRI machines, and could cut energy losses in power transmission. But most superconductors must be cooled to temperatures only a few kelvin above absolute zero, a costly procedure limiting their practical applications. In the past decade, tremendous advances have been made in producing materials that become superconductors at relatively high temperatures. There is hope that room temperature superconductors may someday be manufactured.
Superconductivity was discovered accidentally in 1911 by the Dutch physicist H. Kamerlingh Onnes (1853–1926) when he used liquid helium to cool mercury. Onnes had been the first person to liquefy helium a few years earlier and was surprised to observe the resistivity of a mediocre conductor like mercury drop to zero at a temperature of 4.2 K. We define the temperature at which and below which a material becomes a superconductor to be its critical temperature , denoted by \(T_{c}\). (See Figure \(\PageIndex{1}\).) Progress in understanding how and why a material became a superconductor was relatively slow, with the first workable theory coming in 1957. Certain other elements were also found to become superconductors, but all had \(T_{c}\)'s less than \(10 K\), which are expensive to maintain. Although Onnes received a Nobel prize in 1913, it was primarily for his work with liquid helium.
In 1986, a breakthrough was announced -- a ceramic compound was found to have an unprecedented \(T_{c}\) of 35 K. It looked as if much higher critical temperatures could be possible, and by early 1988 another ceramic (this of thallium, calcium, barium, copper, and oxygen) had been found to have \(T_{c} = 125 K\) (see Figure \(\PageIndex{2}\).) The economic potential of perfect conductors saving electric energy is immense for \(T_{c}\)'s above \(77 K\), since that is the temperature of liquid nitrogen. Although liquid helium has a boiling point of \(4 K\) and can be used to make materials superconducting, it costs about $5 per liter. Liquid nitrogen boils at \(77 K\), but only costs about $0.30 per liter. There was general euphoria at the discovery of these complex ceramic superconductors, but this soon subsided with the sobering difficulty of forming them into usable wires. The first commercial use of a high temperature superconductor is in an electronic filter for cellular phones. High-temperature superconductors are used in experimental apparatus, and they are actively being researched, particularly in thin film applications.
The search is on for even higher \(T_{c}\) superconductors, many of complex and exotic copper oxide ceramics, sometimes including strontium, mercury, or yttrium as well as barium, calcium, and other elements. Room temperature (about \(293 K\)) would be ideal, but any temperature close to room temperature is relatively cheap to produce and maintain. There are persistent reports of \(T_{c}\)'s over \(200 K\) and some in the vicinity of \(270 K\). Unfortunately, these observations are not routinely reproducible, with samples losing their superconducting nature once heated and recooled (cycled) a few times (see Figure \(\PageIndex{3}\)). They are now called USOs or unidentified superconducting objects, out of frustration and the refusal of some samples to show high \(T_{c}\) even though produced in the same manner as others. Reproducibility is crucial to discovery, and researchers are justifiably reluctant to claim the breakthrough they all seek. Time will tell whether USOs are real or an experimental quirk.
The theory of ordinary superconductors is difficult, involving quantum effects for widely separated electrons traveling through a material. Electrons couple in a manner that allows them to get through the material without losing energy to it, making it a superconductor. High-\(T_{c}\) superconductors are more difficult to understand theoretically, but theorists seem to be closing in on a workable theory. The difficulty of understanding how electrons can sneak through materials without losing energy in collisions is even greater at higher temperatures, where vibrating atoms should get in the way. Discoverers of high \(T_{c}\) may feel something analogous to what a politician once said upon an unexpected election victory -- "I wonder what we did right?"
Summary
- High-temperature superconductors are materials that become superconducting at temperatures well above a few kelvin.
- The critical temperature \(T_{c}\) is the temperature below which a material is superconducting.
- Some high-temperature superconductors have verified \(T_{c}\)'s above \(125 K\), and there are reports of \(T_{c}\)'s as high as \(250 K\).
Glossary
- Superconductors
- materials with resistivity of zero
- critical temperature
- the temperature at which and below which a material becomes a superconductor


2.3: CHAPTER 3- AN OVERVIEW OF MENTAL ILLNESS
Indicators Associated with Disorders of Thinking: Schizophrenia
Key Points for Caregivers
1. With schizophrenia, all those who care for verbal clients must try to know the content of any hallucination or delusion their client is experiencing or has experienced. A typical hallucination might involve a deep, loud commanding male voice repeatedly telling a client that he or she is “worthless and must die.” Caregivers are expected to pose a clear question, such as “Are you hearing voices right now?” when clients are talking to themselves.
2. Caregivers of non-verbal clients must try to determine if hallucinations or delusions are occurring . Indicators of hallucinations include
a. Staring to the side and nodding and making hand motions as though listening to a conversation others do not hear.
b. Physically attacking an unseen other person.
c. Staring with an angry or frightened expression at strangers or well-liked companions, in a situation that does not require those emotions.
d. Covering the eyes or ears as if to protect oneself, when threats are not present.
e. Frowning as though something smelled or tasted foul.
f. Dressing in protective ways such as wrapping on extra scarves or blankets when the weather does not require it.
3. The nature of schizophrenia prevents the client from understanding that the voices or other hallucinations or delusions are not real. The only treatment that is effective in decreasing the thought changes in schizophrenia is antipsychotic medication. Without medication, trying to orient clients to reality can bring on profound anxiety and even aggressive actions. Caregivers must know what psychiatric medications have been prescribed .
4. The major side effects of psychiatric medication are a further challenge to treating schizophrenia. Hallucinations and delusions often include the belief that antipsychotic medication is poison . In response to this belief, psychotic clients frequently pretend to swallow pills, or cheek . Given this unchangeable reluctance to swallowing pills, clients often receive long-acting antipsychotic medications intra-muscularly during monthly clinic visits. However, caregivers must always watch clients swallow their psychiatric medications .
Indicators Associated with Disorders of Thinking: Psychosis
Key Points for Caregivers
- With psychosis, determine whether clients know that fantasy conversations are not real.
- Rule out dehydration , particularly in clients who are elderly.
- Ask whether the client has been having seizures or has a seizure disorder .
- Note whether a new medication or new medical condition is present.
- Document any street drug use, as many drugs induce psychotic-like behaviour.
Indicators Associated with Disorders of Thinking: Dementia
Key Points for Caregivers
- Keep records of changes in behaviour and loss of previous abilities. This is especially important to health care workers diagnosing dementia. Therefore, maintaining clear records of how clients function throughout their adult life is useful. These records can be formal medical charts obtained from physicians, or they can be informal records obtained from family members or clients themselves. Scrapbooks, photo albums, video home movies, and audio recordings will illustrate how clients spoke, moved, and responded when they were well and healthy. Comparing a previous picture, audio, or video with a current cell phone capture of a client can clarify changes that are happening.
- Record specific examples of physical weakening, particularly in speaking and walking. For example, identify how a client’s gait or how they walk is changing. Keep a record of any falls, stumbles, or times when clients seem to lose their balance.
- Prepare for and seek medical help immediately if seizures occur. A seizure in someone previously unaffected, and that is not part of a medical condition, can indicate dementia.
- Understand and identify how often confabulation answers are occurring. Confabulation means making up answers without intending to lie. Knowing that clients with dementia are not lying or making things up on purpose can help caregivers understand that this behaviour is part of a psychiatric disorder and not acting-out behaviour.
- Understand and identify how often sundowning is occurring. Sundowning means increased agitation in the evening. Clients may seem to be expressing anger by behaviours such as screaming and yelling, but it is important to understand that this behaviour is likely a response to an intense and constant inner fear that clients are unable to escape.
- Create and communicate supports that help memory lapses. People with dementia are forgetful, get lost, and can have difficulty recognizing friends, family, and staff. Whenever possible, create cues to help with memory loss, such as calendars of events, photo collections, or scrapbooks. Ensure that these cues are consistent and that as many people as possible in the client’s life know about them.
Indicators Associated with Disorders of Mood: Vegetative Shift
Key Points for Caregivers
Vegetative shift is a term used by mental health professionals to describe problems associated with depressive disorders. A vegetative shift occurs when vegetative signs shift or change. Critical vegetative signs include affect, energy, pleasure, appetite, sleep, and thoughts of suicide. A memory aid for indicators of vegetative shift is “A E P A S S.”
Use the “A E P A S S” (Affect, Energy, Pleasure, Appetite, Sleep, Suicide) memory aid to document a shift in vegetative signs.
- “A” – an Affect of sadness and poor concentration. Identify sad facial, postural, and emotional responses that last for weeks at a time and that do not seem to fit the context. Sadness in clients may or may not be a response to something that has happened. Clients may show their depression through crying, becoming withdrawn and non-responsive, or becoming agitated and verbally and physically aggressive.
- “E” – Energy loss and fatigue. Write down the number of times clients are refusing to leave their beds, take care of activities of daily living such as bathing and dressing, and attend work or leisure activities. Include times when either constipation or incontinence occurs in relation to lacking the energy to go to the bathroom. Include the number of hours clients spend sitting or lying down for long periods of time just watching TV or doing nothing.
- “P” – Pleasure or interest. Notice whether clients are no longer taking pleasure in activities they once enjoyed. Notice also when clients with a bipolar disorder are cycling into a manic or hyperactive state, when they may carry out pleasurable activities impulsively. In particular, monitor reckless behaviour in spending money and sexual activity.
- “A” – Appetite changes. Appetite can increase or decrease in depressive disorders. Carefully record client weight and identify any gains or losses. Tantrums at meals, and stealing or hoarding food for constant nibbling, can reflect a need to soothe the emotional distress of depression. In contrast, refusing to take time to eat can reflect the hyperactivity associated with a manic state.
- “S” – Sleep disturbances. Keep a record of the number of hours clients sleep each night, including the time they go to bed, the number of times they get up in the night, and the time they wake up. Difficulty falling asleep can be an indicator of anxiety. Waking up early can be an indicator of depression. Sleeping in late can be a response to dysthymia, where people feel sad in the morning but then feel better as the day progresses. Remaining in bed and sleeping or dozing for long periods of time during both night and day can be a way of withdrawing that is often associated with depression. In contrast, going to bed late, getting up frequently in the night, and getting out of bed early can indicate a pattern of hyperactivity associated with a manic state.
- “S” – Suicidal thinking. Ask verbal clients if they have thought about taking their own life, if they have a plan to do so, and what (if anything) stops them. Assess if clients seem to speak often about death when such discussions are out of context.  Important: Remove any objects that could be used for self-harm.
Indicators Associated with Disorders of Mood: Anxiety, Post-traumatic Stress Disorder (PTSD)
Key Points for Caregivers
- Monitor sleeping and identify whether nightmares are occurring . When possible, identify what the nightmares are about.
- Record situations when clients seem fearful , particularly when there does not seem to be anything or anyone around who could hurt them. Notice if clients avoid certain situations or individuals by verbal and non-verbal resistance and behaviours.
- Provide records of known traumatic events to caregivers and family members. Exchange information about these events to distinguish whether they are new traumas or flashbacks .
Indicators Associated with Disorders of Mood: Anxiety, Obsessive-compulsive Disorder (OCD)
Key Points for Caregivers
- Delay rather than interrupt ritualistic behaviours. Expect that clients may respond with aggression when re-directed away from their repetitive behaviours. When caregivers view the behaviours through the eyes of clients, caregivers can acknowledge a client’s belief that these behaviours are the only possible relief from unbearable anxiety.
- Prepare for and seek medical help immediately if seizures occur , particularly if clients have or have the potential for seizure disorders and are taking the antidepressant medication clomipramine (also called Anafranil).
- Make comfort measures available when ritualistic behaviours result in physical symptoms. For example, hand lotion for excessive hand washing, and padding or helmets for head banging.
Indicators Associated with Disorders of Behaviour: Borderline Personality Disorder
Key Points for Caregivers
- Gather as much information as possible about clients’ patterns of over-reacting and behaviour that is harmful to self or others. Identify if the patterns began occurring at a young age and whether any elements of the behaviour have changed and improved over time and with support.
- With borderline personality disorder, consistent communication among caregivers is critically important. Divisions among caregivers can occur if clients split or view individuals around them only as all good or all bad.


1.3: Function Notation and Simplify Expressions
The goal of this section is to practice function notation. Functions have many interconnected mathematical concepts. Therefore, more detail about functions will emerge in your Precalculus course. This section will practice the correspondence of inputs to outputs using function notation, giving further practice with the properties introduced in previous sections.
The following three equations express three different mathematical rules. The rule creates a correspondence between \(x\)-values and \(y\)-values.
| Equation | The Rule In Words |
| \(y = 2x + 6\) | Double the \(x\)-value then add \(6\). |
| \(y = \dfrac{x}{2} − 4\) | Take half of the \(x\)-value then subtract \(4\). |
| \(y = x^2 -10\) | Square the \(x\)-value then subtract \(10\). |
A function is a rule that assigns each input to exactly one output
A table displays the correspondence between inputs (\(x\)-values) and outputs (\(y\)-values). The three functions above are shown below using \(x\)-\(y\) tables. An \(x\)-value is chosen, the rule is followed, and a \(y\)-value results. Each \(y\)-value is computed according to the function’s rule.
| \(x\) | \(y = 2x + 6\) |
|---|---|
| \(-10\) | \(2(-10)+6 = -14\) |
| \(-3\) | \(2(-3)+6 = 0\) |
| \(0\) | \(2(0) + 6 = 6\) |
| \(2\) | \(2(2) + 6 =10\) |
| \(x\) | \(y = \dfrac{x}{2} − 4\) |
|---|---|
| \(-6\) | \(−6 ÷ 2 − 4 = −7\) |
| \(0\) | \(0 ÷ 2 − 4 = −4\) |
| \(6\) | \(6 ÷ 2 − 4 = −1\) |
| \(18\) | \(18 ÷ 2 − 4 = 5\) |
| \(x\) | \(y = x^2 -10\) |
|---|---|
| \(-1\) | \((−1)^2 − 10 = −9\) |
| \(0\) | \(0^2 − 10 = −10\) |
| \(1\) | \(1^2 − 10 = −9\) |
| \(4\) | \(4^2 − 10 = 6\) |
Since the output of the function depends on the input, the \(y\)-value is called the dependent variable . Function notation emphasizes this dependence by replacing the variable \(y\) with \(f(x)\).
| \(x\)-\(y\) notation | Function notation | Read out loud |
| \(y = 2x + 6\) | \(f(x) = 2x+6\) | “\(f\) of \(x\) equals two \(x\) plus six” |
Let \(f(x) = 2x + 6\). Evaluate of each of the following.
- \(f(−1)\)
- \(f \left( \dfrac{1}{2} \right)\)
- \(f(3a)\)
Solution
In each problem, the input, or \(x\)-value, is given inside the parentheses. We substitute the given \(x\)-value into the function \(f(x) = 2x + 6\).
- \(f(−1) = 2(−1) + 6 = −2 + 6 = 4\). Therefore, \(f(−1) = 4\).
- \(f \left( \dfrac{1}{2} \right) = 2 \left( \dfrac{1}{2} \right) + 6 = 1 + 6 = 7\). Therefore, \(f \left( \dfrac{1}{2} \right) = 7\).
- The \(x\)-value is replaced by \(3a\). This will yield an expression rather than a numerical value: \(f(3a) = 2(3a) + 6 = 6a + 6\). Therefore, \(f(3a) = 6a + 6\).
Functions are typically named with the letters \(f\), \(g\), and \(h\), but functions can take on other letter-names as well. Using different letter-names for functions can help us refer to several different functions in one problem. Example \(1.3.2\) makes use of this concept.
Let \(h(x) = f(x) + g(x)\) where \(f(x) = 3x^2\) and \(g(x) = 5x − 9\). Evaluate each of the following:
- \(h(−4)\)
- \(h \left( \dfrac{1}{2} \right)\)
- \(h(a + 1)\)
Solution
The function \(h\) is defined as the sum of \(f\) and \(g\). Plug the given input-value into each function, evaluate to find each output, and take the sum.
- \(h(−4) = f(−4) + g(−4) = \underbrace{3(−4)^2}_{f(−4)} + \underbrace{5( − 4 ) − 9}_{g(−4)} = 3 \cdot 16 + (−20 − 9) = 48 − 29 = 19\)
Therefore, \(h(−4) = 19\).
- \(h \left( \dfrac{1}{2} \right) = f \left( \dfrac{1}{2} \right) + g \left( \dfrac{1}{2} \right) = \underbrace{3 \left( \dfrac{1}{2} \right)^2}_{f(\frac{1}{2})} + \underbrace{5 \left( \dfrac{1}{2} \right) -9}_{g(\frac{1}{2})} = 3\left( \dfrac{1}{4} \right) + \dfrac{5}{2} - 9 = \dfrac{3}{4} + \dfrac{10}{4} - \dfrac{36}{4} = -\dfrac{23}{4}\)
Therefore, \(h \left( \dfrac{1}{2} \right) = -\dfrac{23}{4}\)
- Replace \(x\) with \(a + 1\), then simplify. \(h(a + 1) = f(a + 1) + g(a + 1)\)
\(\begin{array} &&=\underbrace{3(a+1)^2}_{f(a+1)} + \underbrace{5(a+1) -9}_{g(a+1)} \\ &= 3(a + 1)(a + 1) + 5a + 5 − 9 \\ &= 3(a^2 + 2a + 1) + 5a − 4 \\ &= 3a^2 + 6a + 3 + 5a − 4 \\ &= 3a^2 + 6a + 5a + 3 − 4 \\ h(a + 1) &= 3a^2 + 11a − 1 \end{array}\)
Let \(f(x) = 2x^2 − 4x + 1\). Evaluate each of the following:
- \(f(−3)\)
- \(f(a + 2)\)
- \(f(a + 2) − f(a)\)
Solution
- Replace each \(x\) with \(x = −3\).
\(f(−3) = 2(−3) 2 − 4(−3) + 1 = 2 \cdot 9 + 12 + 1 = 18 + 12 + 1 = 31\)
Therefore, \(f(−3) = 31\).
- Replace each \(x\) with \(a + 2\). Then simplify.
\(\begin{array} &f(a + 2) &= 2(a + 2) 2 − 4(a + 2) + 1 &\\ &= 2(a^2 + 4a + 4) − 4a − 8 + 1 &\text{Use Special Products and the Distributive Property} \\ & = 2a^2 + 8a + 8 − 4a − 8 + 1& \\ &= 2a^2 + 8a − 4a + 8 − 8 + 1 &\text{Rearrange terms to combine like terms} \\ f(a + 2) &= 2a^2 + 4a + 1 & \end{array}\)
- We will subtract \(f(a)\) from the answer to part b.
\(\begin{array} &&\underbrace{2a^2 + 4a + 1}_{f(a+2)} − \underbrace{(2a^2 − 4a + 1 )}_{f(a)} &\text{Use answer from part b: \(f(a + 2) = 2a^2 + 4a + 1\)} \\ &= 2a^2 + 4a + 1 − 2a^2 + 4a − 1 &\text{Subtract a quantity, so subtract each term.} \\ &= 2a^2 − 2a^2 + 4a + 4a + 1 − 1 &\text{Rearrange terms to combine like terms.} \end{array}\)
Answer \(f(a + 2) − f(a) = 8a\)
Let \(f(x) = 3x − 4\). Evaluate each of the following.
- \(f(a^2)\)
- \([f(a)]^2\)
Solution
The order of operations will yield different results.
- \(f(a^2)\) indicates \(x = a^2\). Therefore, \(f(a^2) = 3a^2 − 4\).
- \([f(a)]^2\) indicates \(x = a\). After substitution, square the result.
\(\begin{array} &&[f(a)]^2 = (3a − 4)^2 &\text{Substitute \(x = a\) into the function \(f\).} \\ &[f(a)]^2 = 9a^2 − 24a + 16 &\text{Use the Special Products Formula.} \end{array}\)
Try It! (Exercises)
For #1-13, evaluate the functions using \(f\) and \(g\) as defined below. Do not use a calculator.
\(f(x) = – 2x + 1\)
\(g(x) = x^2 + 3x − 2\)
- \(f(3)\)
- \(g(1)\)
- \(f \left( \dfrac{1}{2} \right)\)
- \(g(−2)\)
- \(f(−1) − g(3)\)
- \(g(2a)\)
- \(f(3a)\)
- \(f(a − 4)\)
- \(g(a − 1)\)
- \(g(a^2)\)
- \([f(a)]^2\)
- \(g(a) − f(a + 1)\)
- \(g(a) − f(a^2)\)
14. Let \(h(x) = f(x) + g(x)\). Evaluate each of the following:
- \(h(−5)\)
- \(h(4a)\)
- \(h(a − 3)\)
For #15-34, evaluate the functions using \(f\) and \(g\) as defined below. Do not use a calculator.
\(f(x) = \dfrac{x}{x+1}\)
\(g(x) = \dfrac{4x}{x+2}\)
- \(f(3)\)
- \(f(−3)\)
- \(g(2)\)
- \(g(−2)\)
- \(f(2) + g(4)\)
- \(f(0) − g(6)\)
- \([f(1)]^2\)
- \([g(3)]^2\)
- \(f \left( \dfrac{1}{2} \right)\)
- \(g \left( \dfrac{1}{2} \right)\)
- \(f(a − 1)\)
- \(g(a − 1)\)
- \( [g(1)]^{−2}\)
- \([f(4)]^{−2}\)
- \([f(−2)]^{−1}\)
- \([g(−1)]^{−1}\)
- \(\left[g \left( \dfrac{1}{4} \right) \right]^{−1}\)
- \([f(5)]^{−1} + [g(5)]^{−1}\)
- \([f(5) + g(5)]^{−1}\)
- \(\dfrac{f(a)}{g(a)}\)


3.8: Open and Closed Sets. Neighborhoods
I. Let \(A\) be an open globe in \((S, \rho)\) or an open interval \((\overline{a}, \overline{b})\) in \(E^{n} .\) Then every \(p \in A\) can be enclosed in a small globe \(G_{p}(\delta) \subseteq A(\) Figures 7 and 8\()\). (This would fail for "boundary" points; but there are none inside an open \(G_{q}\) or \((\overline{a}, \overline{b}) . )\).
This suggests the following ideas, for any \((S, \rho)\).
A point \(p\) is said to be interior to a set \(A \subseteq(S, \rho)\) iff \(A\) contains some \(G_{p} ;\) i.e., \(p,\) together with some globe \(G_{p},\) belongs to \(A .\) We then also say that \(A\) is a neighborhood of \(p .\) The set of all interior points of \(A\) ("the interior of \(A^{\prime \prime}\) is denoted \(A^{0} .\) Note: \(\emptyset^{0}=\emptyset\) and \(S^{0}=S !\)
\(\mathrm{A}\) set \(A \subseteq(S, \rho)\) is said to be open iff \(A\) coincides with its interior \(\left(A^{0}=A\right) .\) Such are \(\emptyset\) and \(S .\)
(1) As noted above, an open globe \(G_{q}(r)\) has interior points only, and thus is an open set in the sense of Definition \(2 .\) (See Problem 1 for a proof.)
(2) The same applies to an open interval \((\overline{a}, \overline{b})\) in \(E^{n} .\) (See Problem \(2 . )\)
(3) The interior of any interval in \(E^{n}\) never includes its endpoints \(\overline{a}\) and \(\overline{b}\). In fact, it coincides with the open interval \((\overline{a}, \overline{b}) .\) (See Problem \(4 . )\)
(4) The set \(R\) of all rationals in \(E^{1}\) has no interior points at all \(\left(R^{0}=\emptyset\right)\) because it cannot contain any \(G_{p}=(p-\varepsilon, p+\varepsilon) .\) Indeed, any such \(G_{p}\) contains irrationals (see Chapter 2, §§11-12, Problem 5\(),\) so it is not entirely contained in \(R .\)
(Hausdorff property). Any two points \(p\) and \(q\) \((p \neq q)\) in \((S, \rho)\) are centers of two disjoint globes.
More precisely,
\[(\exists \varepsilon>0) \quad G_{p}(\varepsilon) \cap G_{q}(\varepsilon)=\emptyset.\]
- Proof
-
As \(p \neq q,\) we have \(\rho(p, q)>0\) by metric axiom \(\left(\mathrm{i}^{\prime}\right) .\) Thus we may put
\[\varepsilon=\frac{1}{2} \rho(p, q)>0.\]
It remains to show that with this \(\varepsilon, G_{p}(\varepsilon) \cap G_{q}(\varepsilon)=\emptyset\).
Seeking a contradiction, suppose this fails. Then there is \(x \in G_{p}(\varepsilon) \cap G_{q}(\varepsilon)\) so that \(\rho(p, x)<\varepsilon\) and \(\rho(x, q)<\varepsilon .\) By the triangle law,
\[\rho(p, q) \leq \rho(p, x)+\rho(x, q)<\varepsilon+\varepsilon=2 \varepsilon ; \text{ i.e., } \rho(p, q)<2 \varepsilon,\]
which is impossible since \(\rho(p, q)=2 \varepsilon . \square\)
Note. A look at Figure 9 explains the idea of this proof, namely, to obtain two disjoint globes of equal radius, it suffices to choose \(\varepsilon \leq \frac{1}{2} \rho(p, q) .\) The reader is advised to use such diagrams in \(E^{2}\) as a guide.
II. We can now define closed sets in terms of open sets.
A set \(A \subseteq(S, \rho)\) is said to be closed iff its complement \(-A=S-A\) is open, i.e., has interior points only.
That is, each \(p \in-A\) (outside \(A )\) is in some globe \(G_{p} \subseteq-A\) so that
\[A \cap G_{p}=\emptyset.\]
(Continued).
(5) The sets \(\emptyset\) and \(S\) are closed, for their complements, \(S\) and \(\emptyset,\) are open, as noted above. Thus a set may be both closed and open ("clopen").
(6) All closed globes in \((S, \rho)\) and all closed intervals in \(E^{n}\) are closed sets by Definition \(3 .\) Indeed (see Figures 9 and \(10 ),\) if \(A=\overline{G}_{q}(r)\) or \(A=[\overline{a}, \overline{b}]\), then any point \(p\) outside \(A\) can be enclosed in a globe \(G_{p}(\delta)\) disjoint from \(A ;\) so, by Definition \(3, A\) is closed (see Problem 12\()\).
(7) A one-point set \(\{q\}\) (also called "singleton") in \((S, \rho)\) is always closed, for any \(p\) outside \(\{q\}(p \neq q)\) is in a globe disjoint from \(\{q\}\) by Theorem 1 In a discrete space (§§11,) Example (3)), \(\{q\}\) is also open since it is an open \(g\) lobe, \(\{q\}=G_{q}\left(\frac{1}{2}\right)(\) why? \() ;\) so it is "clopen. " Hence, in such a space, all sets are "clopen". For \(p \in A\) implies \(\{p\}=G_{p}\left(\frac{1}{2}\right) \subseteq A ;\) similarly for \(-A .\) Thus \(A\) and \(-A\) have interior points only, so both are open.
(8) The interval \((a, b]\) in \(E^{1}\) is neither open nor closed. (Why?)
III. (The rest of this section may be deferred until Chapter (4, §10.)
The union of any finite or infinite family of open sets \(A_{i}(i \in I)\), denoted
\[\bigcup_{i \in I} A_{i},\]
is open itself. So also is
\[\bigcap_{i=1}^{n} A_{i}\]
for finitely many open sets. (This fails for infinitely many sets \(A_{i} ;\) see Problem 11 below.)
- Proof
-
We must show that any point \(p\) of \(A=\bigcup_{i} A_{i}\) is interior to \(A\).
Now if \(p \in \bigcup_{i} A_{i}, p\) is in some \(A_{i},\) and it is an interior point of \(A_{i}\) (for \(A_{i}\) is open, by assumption). Thus there is a globe
\[G_{p} \subseteq A_{i} \subseteq A,\]
as required.
For finite intersections, it suffices to consider two open sets \(A\) and \(B\) (for \(n\) sets, all then follows by induction). We must show that each \(p \in A \cap B\) is interior to \(A \cap B .\)
Now as \(p \in A\) and \(A\) is open, we have some \(G_{p}\left(\delta^{\prime}\right) \subseteq A .\) Similarly, there is \(G_{p}\left(\delta^{\prime \prime}\right) \subseteq B .\) Then the smaller of the two globes, call it \(G_{p},\) is in both \(A\) and \(B,\) so
\[G_{p} \subseteq A \cap B\]
and \(p\) is interior to \(A \cap B,\) indeed. \(\square\)
If the sets \(A_{i}(i \in I)\) are closed, so is
\[\bigcap_{i \in I} A_{i}\]
(even for infinitely many sets). So also is
\[\bigcup_{i=1}^{n} A_{i}\]
for finitely many closed sets \(A_{i} .\) (Again, this fails for infinitely many sets \(A_{i} . )\)
- Proof
-
Let \(A=\bigcap_{i \in I} A_{i} .\) To prove that \(A\) is closed, we show that \(-A\) is open.
Now by set theory (see Chapter 1, §§1-3, Theorem 2) ,
\[-A=-\bigcap_{i} A_{i}=\bigcup_{i}\left(-A_{i}\right),\]
where the \(\left(-A_{i}\right)\) are open (for the \(A_{i}\) are closed \() .\) Thus by Theorem \(2,-A\) is open, as required.
The second assertion (as to \(\bigcup_{i=1}^{n} A_{i} )\) follows quite similarly. \(\square\)
\(A\) nonempty set \(A \subseteq(S, \rho)\) is open iff \(A\) is a union of open globes.
For if \(A\) is such a union, it is open by Theorem \(2 .\) Conversely, if \(A\) is open, then each \(p \in A\) is in some \(G_{p} \subseteq A .\) All such \(G_{p}(p \in A)\) cover all of \(A,\) so \(A \subseteq \bigcup_{p \in A} G_{p} .\) Also, \(\bigcup_{p \in A} G_{p} \subseteq A\) since all \(G_{p}\) are in \(A .\) Thus
\[A=\bigcup_{p \in A} G_{p}.\]
Every finite set \(F\) in a metric space \((S, \rho)\) is closed.
- Proof
-
If \(F=\emptyset, F\) is closed by Example \((5) .\) If \(F \neq \emptyset,\) let
\[F=\left\{p_{1}, \ldots, p_{n}\right\}=\bigcup_{k=1}^{n}\left\{p_{k}\right\}.\]
Now by Example \((7),\) each \(\left\{p_{k}\right\}\) is closed; hence so is \(F\) by by theorem \(3 . \square\)
Note. The family of all open sets in a given space \((S, \rho)\) is denoted by \(\mathcal{G}\); that of all closed sets, by \(\mathcal{F} .\) Thus \(" A \in \mathcal{G}^{\prime \prime}\) means that \(A\) is open; "A \(\in \mathcal{F}^{\prime \prime}\) means that \(A\) is closed. By Theorems 2 and \(3,\) we have
\[(\forall A, B \in \mathcal{G}) \quad A \cup B \in \mathcal{G} \text{ and } A \cap B \in \mathcal{G};\]
similarly for \(\mathcal{F} .\) This is a kind of "closure law." We say that \(\mathcal{F}\) and \(\mathcal{G}\) are "closed under finite unions and intersections."
In conclusion, consider any subspace \((A, \rho)\) of \((S, \rho) .\) As we know from §11 it is a metric space itself, so it has its own open and closed sets (which must consist of points of \(A\) only \() .\) We shall now show that they are obtained from those of \((S, \rho)\) by intersecting the latter sets with \(A .\)
Let \((A, \rho)\) be a subspace of \((S, \rho) .\) Then the open (closed) sets in \((A, \rho)\) are exactly all sets of the form \(A \cap U,\) with \(U\) open \((\)closed\()\) in \(S\).
- Proof
-
Let \(G\) be open in \((A, \rho) .\) By Corollary \(1, G\) is the union of some open globes \(G_{i}^{*}(i \in I)\) in \((A, \rho) .\) (For brevity, we omit the centers and radii; we also omit the trivial case \(G=\emptyset .\)
\[G=\bigcup_{i} G_{i}^{*}=\bigcup_{i}\left(A \cap G_{i}\right)=A \cap \bigcup_{i} G_{i},\]
by set theory (see Chapter 1, §§1-3,\) Problem 9).
Again by Corollary \(1, U=\bigcup_{i} G_{i}\) is an open set in \((S, \rho) .\) Thus \(G\) has the form
\[A \cap \bigcup_{i} G_{i}=A \cap U,\]
with \(U\) open in \(S,\) as asserted.
Conversely, assume the latter, and let \(p \in G .\) Then \(p \in A\) and \(p \in U .\) As \(U\) is open in \((S, \rho),\) there is a globe \(G_{p}\) in \((S, \rho)\) such that \(p \in G_{p} \subseteq U .\) As \(p \in A,\) we have
\[p \in A \cap G_{p} \subseteq A \cap U.\]
However, \(A \cap G_{p}\) is a globe in \((A, \rho),\) call it \(G_{p}^{*} .\) Thus
\[p \in G_{p}^{*} \subseteq A \cap U=G;\]
i.e., \(p\) is an interior point of \(G\) in \((A, \rho) .\) We see that each \(p \in G\) is interior to \(G,\) as a set in \((A, \rho),\) so \(G\) is open in \((A, \rho) .\)
This proves the theorem for open sets. Now let \(F\) be closed in \((A, \rho) .\) Then by Definition \(3, A-F\) is open in \((A, \rho) .\) (Of course, when working in \((A, \rho)\), we replace \(S\) by \(A\) in taking complements.) Let \(G=A-F,\) so \(F=A-G,\) and \(G\) is open in \((A, \rho) .\) By what was shown above, \(G=A \cap U\) with \(U\) open in \(S\).
Thus
\[F=A-G=A-(A \cap U)=A-U=A \cap(-U)\]
by set theory. Here \(-U=S-U\) is closed in \((S, \rho)\) since \(U\) is open there. Thus \(F=A \cap(-U),\) as required.
The proof of the converse (for closed sets) is left as an exercise. \(\square\)


1.3: Appendix B- Title 22 Licensing Regulation Highlights
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Appendix B: Title 22 Licensing Regulation Highlights 762
101152 DEFINITIONS
- Child Care Center means any child care facility of any capacity, other than a Family Child Care Home, in which less than 24-hour per day, non-medical care and supervision are provided to children in a group setting
- The Department means the California Department of Social Services or agency which is authorized to assume licensing responsibilities.
101156 LICENSE REQUIRED
- Unless a child care arrangement is exempt from licensure (101158), no adult, partnership, corporation, public agency or other governmental entity shall operate, establish, manage, conduct or provide care and supervision without a valid license from the Department.
101160 POSTING OF LICENSE
- The license shall be posted in a prominent, publicly accessible location in the center.
101167 TRANSFER AND SALE
- A license is not transferable.
- The licensee shall provide written notice to the department and to the child’s parent/legal guardian of the intent to sell the day care center at least 20 days prior to the transfer of the property or business.
- The seller shall notify, in writing, a prospective buyer of the necessity to obtain a license.
- The prospective buyer shall submit an application for a license within five days of the acceptance of the offer by the seller.
101169 APPLICATION FOR LICENSE
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101170
CRIMINAL RECORD CLEARANCE
- The Department will conduct a criminal record review of all persons working in a child care facility including:
- Adults responsible for administration or supervision of staff.
- Any person, other than a child, residing in the facility.
- Any person who provides care and supervision to children.
- Any staff person who has contact with the children.
- Relatives and legal guardians of a child in the facility are exempt.
- A volunteer or student who is always directly supervised by a fingerprinted staff, and who spends no more than 16 hours per week at the facility is exempt.
- Prior to employment, residence or initial presence in the child care facility, all individuals subject to a criminal record review shall obtain a Department of Justice clearance, or request a transfer of a current clearance to be associated with the facility.
101170.2 CHILD ABUSE CENTRAL INDEX
- A Child Abuse Central Index review shall be conducted on the applicant and all individuals subject to a criminal record review prior to licensure, employment or initial presence in the facility.
101171 FIRE CLEARANCE
- All Child Care Centers shall secure and maintain a fire clearance.
101173 PLAN OF OPERATION
- Each licensee shall keep on file a current, written, definitive plan of operation. This document must contain the program methods; goals; admission policies, procedures, and agreement; the administrative organization and staffing plan; a sketch of the building; sample menus and transportation arrangements.
101174 DISASTER AND MASS CASUALTY PLAN
- Each licensee shall have a disaster plan of action in writing.
- Disaster drills shall be documented and conducted every six months.
101175 WAIVERS AND EXCEPTIONS FOR PROGRAM FLEXIBILITY
- The Department has the authority to approve the use of alternate concepts, programs, services, equipment, space, qualifications, ratios and demonstration projects when there is an alternative for safe and adequate services submitted in writing with substantiating evidence to support the request.
101179 CAPACITY DETERMINATION
- A license is issued for a specific capacity which is the maximum number of children that can be cared for at any given time. The number of children is determined by the fire clearance; the physical features of the Child Care Care Center, including available space; and the available staff to meet the care and supervision needs of the children.
101182 ISSUANCE/TERM OF LICENSE
- A separate license is issued for each age component.
- At lease one director or teacher at the center shall have 15 hours of training on preventive health practices, including pediatric cardiopulmonary resuscitation and pediatric first aid. A staff member with certification in pediatric CPR and first aid shall be present at all times.
101187 LICENSING FEES
- The licensee shall be charged application and annual fees.
101193 DEFIC IENCIES IN COMPLIANCE
- If during a licensing evaluation the evaluator determines that a deficiency exists, a notice of deficiency will be issued in writing, unless the deficiency is corrected during the visit.
- The person in charge of the facility shall meet with the evaluator to discuss any deficiencies noted and to jointly develop a plan of correction.
101200 INSPECTION AUTHORITY
- The Department has inspection authority to enter and inspect a facility without advance notice.
- The Department has the authority to interview children or staff, and to inspect and audit child or Child Care Center records, without prior consent.
101206 REVOCATION OR SUSPENSION OF LICENSE
- The Department has the authority to suspend or revoke a license.
101208 EXCLUSIONS
- The Department may prohibit an individual from being employed or allowed in a licensed facility or from service as an administrator for the facility.
101212 REPORTING REQUIREMENTS
- The licensee shall report to the Department required information about the center director, any intent to make structural changes to the facility, or any change in the plan of operation that would affect services to children.
- The licensee shall report the following incidents to the Department:
- Any injury to any child that requires medical treatment.
- Any unusual incident or child absence that threatens safety.
- Any suspected physical or psychological abuse of any child.
101213 FINANCES
- The licensee must develop a financial plan to meet operating costs and maintain financial records.
101214 ACCOUNTABI LITY
- The licensee is accountable for the general supervision of the Child Care Center and for the establishment of policies concerning its operation.
101215.1 CHILD CARE CENTER DIRECTOR QUALIFICATIONS
- All centers shall have a director who is responsible for the operation of the center, including compliance with regulations, and communications with the Department. The director shall be on the premises during the hours of operation and shall not accept outside employment that interferes with the duties specified.
- When the director is absent, a fully qualified teacher can act as a substitute.
- Child care center directors shall have completed one of the following prior to employment:
- High school graduation or GED and 15 semester units at an accredited college in specified early childhood education classes. Three of the required units shall be in administration or staff relations and 12 units shall include courses that cover the area of child growth and development; child, family and community; and program/ curriculum and four years of teaching experience in a licensed center or comparable group child care program or
- Two years of experience are required if the director has an AA degree with a major in child development or
- A Child Development Site Supervisor Permit or Child Development Program Director permit issued by the California Commission on Teacher Credentialing.
101216 PERSONNEL REQUIREMENTS
- The director shall complete 15 hours of health and safety training, if necessary, pursuant to Health and Safety Code Section 1596.866.
- Personnel shall be competent to provide necessary services to meet the individual needs of children in care and there shall be enough staff to meet those needs.
- Licensees may utilize volunteers provided that volunteers are supervised and are not included in the staffing plan.
- Center personnel shall be at least 18 years old.
- All personnel shall be in good health and physically and mentally capable of performing assigned tasks.
- A health screening, including a tuberculosis test is required.
- Personnel shall provide for the care and safety of children without physical or verbal abuse, exploitation or prejudice.
101216.1 TEACHER QUALIFICATIONS
- A teacher shall have completed with passing grades a least six postsecondary semester units of specified early childhood education classes, or have a valid Child Development Assistant permit issued by the California Commission on Teacher
- Credentialing. A teacher hired with six units must complete at least two additional units each semester until fully qualified.
- A fully qualified teacher shall have 12 postsecondary semester units in early childhood education from an accredited college and six months of work experience in a licensed Child Care Center or similar program. The units specified shall include courses covering child growth and development; child, family and community; and program/curriculum.
- A teacher shall complete 15 hours of health and safety training, if necessary, pursuant to Health and Safety code, Section 1596.866.
101216.2 TEACHER AIDE QUALIFICATIONS
- An aide in a Child Care Center must be 18 years of age, a high school graduate, or be currently participating in an occupational program at high school.
- An aide shall work only under the direct supervision of a teacher.
- An aide may escort or assist children in going to the bathroom and may supervise napping children without being under the direct supervision of a teacher.
101216.3 TEACHER – CHILD RATIO
- There shall be a ratio of one teacher visually observing and supervising no more than 12 children in attendance. The total number of children shall not exceed licensed capacity.
- The licensee may use teacher aides in a teacher-child ratio of one teacher and one aide for every 15 children.
- A ratio of one fully qualified teacher and one aide for every 18 children is allowed if the aide has six semester units of early childhood education from an accredited college.
- The director may be included in the teacher-child ratio when the director is actually teaching a group of children.
- Licensees shall maintain an up-to-date list of qualified substitutes.
- A teacher should not perform housekeeping or maintenance duties that prevent him/her from performing duties related to providing care and supervision to children.
- Persons employed for clerical, housekeeping and maintenance functions are not included as teachers in the teacher-child ratio.
101216.4 TODDLER COMPONENT
- Licensees serving preschool-age children may create a special program component for children between the ages of 18 months and 30 months.
- A ratio of six children to each teacher shall be maintained for all children in attendance in the toddler program.
- The maximum group size with two teachers, or one fully qualified teacher and one aide shall not exceed 12 toddlers.
- The toddler program must be physically separate.
101218.1 ADMISSION PROCEDURES
- The licensee shall have policies that allow the center to understand the state of the child’s health and development and to assess whether the center can meet the individual needs of the child.
- The child’s authorized representative shall receive written information about the center’s policies including services, activities, hours, fees and procedures to be followed in the case of emergency, illness or injury.
- The licensee shall post the PUB 393, Child Care Center Notification of Parents’ rights Poster, in a prominent accessible area at the center.
101219 ADMISSION AGREEMENTS
- The licensees and the child’s authorized representative shall complete a current individual written admission agreement for the child. This document must specify the basic services, payment provisions, modification conditions, refund conditions, rights of the Department, and termination provisions.
101220 CHILD’S MEDICAL ASSESSMENTS
- Prior to, or within 30 calendar days following enrollment, the licensee will obtain a licensed physician’s written medical assessment of the child. The assessment must be less than one year old.
101220.1 IMMUNIZATIONS
- Prior to admission to a Child Care Center, children shall be immunized against diseases as required by the California Code of Regulations, Title 17.
- The licensee must document and maintain each child’s immunizations records for as long as the child is enrolled.
101221 CHILD’S RECORDS
- A separate, complete and current record for each child must be maintained.
- All information and records obtained from or regarding children are confidential.
101223 PERSONAL RIGHTS
- The licensee shall ensure that each child is accorded the following personal rights:
- To be accorded dignity in his/her personal relationships with staff.
- To receive safe, healthful and comfortable accommodations.
- To be free from corporal or unusual punishment, infliction of pain, humiliation, intimidation, ridicule, coercion, threat, mental abuse or other actions of a punitive nature including interference with functions of daily living such as eating, sleeping or toileting, or withholding of shelter, clothing, medication or aids to physical functioning.
- To be free to attend religious services or activities of his/her choice.
- Not to be locked in any room, building or center premises.
- Not to be placed in any restraining device.
- The center must inform each child’s authorized representative of these rights and provide a copy of the Personal Rights form. This form must also be posted.
101223.2 DISCIPLINE
- Any form of discipline or punishment that violates a child’s personal rights is not permitted regardless of authorized representative consent or authorization.
101224 TELEPHONES
- All Child Care Centers shall have working telephone service onsite.
101225 TRANSPORTATION
- Only drivers licensed for the type of vehicle operated shall be permitted to transport children.
- Motor vehicles used to transport children shall be maintained in safe operating condition.
- All vehicle occupants shall be secured in an appropriate restraint system. Children shall not be left in parked vehicles.
101226 HEALTH-RELATED SERVICES
- The licensee shall immediately notify the child’s authorized representative if the child becomes ill or sustains an injury more serious than a minor cut or scratch.
- The licensee shall document all minor injuries and notify the child’s authorized representative of the nature of the injury when the child is picked up from the center.
- The licensee shall make prompt arrangements for obtaining medical treatment for any child as necessary.
- In centers where the licensee chooses to handle medication:
- Medications must be kept inaccessible to children.
- Prescription medications must be administered in accordance with the label directions as prescribed by the child’s physician and there must be written approval and instructions from the child’s authorized representative before giving medication to the child.
- Nonprescription medications must be administered in accordance with the product label and there must be written approval and instructions from the child’s authorized representative before giving medication to the child.
101226.1 DAILY INSPECTION FOR ILLNESS
- The licensee shall be responsible for ensuring the children with obvious symptoms of illness are not accepted.
- No child shall be accepted without contact between center staff and the person bringing the child to the center.
101226.2 ISOLATION FOR ILLNESS
- A center shall be equipped to isolate and care for any child who becomes ill during the day.
- The child’s authorized representative shall be notified immediately when the child becomes ill enough to require isolation, and shall be asked to pick up the child as soon as possible.
101227 FOOD SERVICE
- Food selection, storage preparation and service shall be safe and healthful and of the quality and quantity necessary to meet the needs of children.
- Meal services are elective.
- Between meals, snacks must be available for all children. Snacks will include servings from two or more of the four major food groups.
- Menus must be in writing and posted at least one week in advance.
- Pesticides and similar toxic substances must not be stored with food.
- Soaps and cleaning compounds must be stored separately from food.
- Kitchens and food areas shall be clean.
- All food shall be protected against contamination.
- Necessary equipment includes a sink, refrigeration, hot and cold running water and storage space. This equipment must be well maintained.
101229 RESPONSIBILITY FOR PROVIDING CARE AND SUPERVISION
- The licensee shall provide care and supervision as necessary to meet the children’s needs. No child shall be left without the supervision of a teacher at any time. Supervision includes visual observation.
101229.1 SIGN IN AND SIGN OUT
- The licensee shall develop, maintain and implement a written procedure to sign the child in/out of the center. The person who signs the child in/out shall use his/her full legal signature and shall record the time of day. All sign in/out sheets shall be kept for one month.
101230 ACTIVIT IES AND NAPPING
- Each center shall provide for a variety of daily activities including quiet and active play, rest and relaxation, eating, and toileting.
- All children shall be given an opportunity to nap or rest without distraction.
- A napping space and a cot or mat must be available for each child under age 5.
- No child shall be forced to stay awake or stay in the napping area longer than the normal napping period.
- A teacher-child ratio of one teacher or aide supervising 24 napping children is permitted, provided that the remaining teachers necessary to meet the overall ratios are immediately available at the center.
101231 SMOKING PROHIBITION
- Smoking is prohibited on the premises of a Child Care Center.
101237 ALTERATIONS TO EXISTING BUILDINGS OR NEW FACILITIES
- Prior to construction or alterations, the licensee shall notify the Department of the proposed change(s).
101238 BUILDINGS AND GROUNDS
- The center shall be clean, safe, sanitary and in good repair at all times.
- All children shall be protected against hazards.
- Licensees shall ensure the inaccessibility of pools and all bodies of water.
- Disinfectants, cleaning solutions, poisons and items that could pose a danger to children shall be stored where inaccessible to children
- Storage areas for poisons shall be locked.
- Firearms and other weapons are not allowed on the premises.
101238.2 OUTDOOR ACT IVITY SPACE
- There shall be at least 75 square feet per child of outdoor activity space. The outdoor space shall provide a shaded rest area and permit children to reach the activity space safely.
- The surface of the activity space shall be in a safe condition and free of hazards.
- The areas around and under climbing equipment, swings, slides and similar equipment shall be cushioned with material that absorbs falls.
- Sandboxes shall be inspected daily and kept free of foreign materials.
- The playground shall be enclosed by a fence at least four feet high.
- Hazardous equipment such as a fuse box shall be inaccessible.
101238.4 STORAGE SPACE
- Each child shall have an individual storage space for personal items.
- There must be storage space in the playrooms for materials and equipment.
101239 FIXTURES, FURNITURE, EQUIPMENT, AND SUPPLIES
- A comfortable temperature shall be maintained at all times.
- All window screens shall be in good repair and free of insects and debris.
- Fireplaces and open-faced heaters shall be inaccessible.
- All containers used for storing solid wastes must have a tight-fitting cover.
- There must be one toilet and hand-washing sink for every 15 children.
- Common towels or washcloths are prohibited.
- Tables and chairs scaled to the size of children must be provided.
- All play equipment and materials used by children must be age-appropriate.
- Furniture and equipment must be maintained in good condition.
- A baby walker shall not be allowed on the premises.
- Permanent playground equipment must be securely anchored to the ground.
101239.1 NAPPING EQUIPMENT
- Cots must be maintained in a safe condition.
- Floor mats used for napping must be at least ¾ inch thick, covered with vinyl or similar material that can be wiped, and marked to distinguish the sleeping side from the floor side.
- Bedding must be individually stored and kept clean.
101239.2 DRINKING WATER
- Drinking water must be readily available both indoors and outdoors.
- Children must be free to drink as they wish.
SCHOOL-AGE CHILD CARE CENTER
101451 GENERAL
- In addition to Child Care Center General Licensing Requirements, school- age centers shall be governed by this chapter.
101471 SCHOOL-AGE CHILD CARE CENTER FIRE CLEARANCE
- In addition to Section 101171, School-age centers located on functioning school sites may submit verification of the school fire inspection. The school fire inspection shall be accepted as sufficient fire clearance for licensing purposes.
101482 ISSUANCE OF A SCHOOL-AGE CHILD CARE CENTER LICENSE
- The Department shall issue a license to an applicant according to Health and Safety Code Section 1597.21, after a completed application has been submitted, and all licensing requirements have been met.
101515 SCHOOL-AGE CHILD CARE CENTER DIRECTOR QUALIFICATIONS AND DUTIES
- In addition to Section 101215.1, the following shall apply:
- All school-age centers shall have a director. In a combination program, the director of the Child Care Center may also direct the school-age component.
- Units and training may be combined to meet the total educational requirement: 15 units or 300 training hours, or any combination thereof.
- As an alternative educational requirement, a director may substitute 6 units in early childhood education with 6 units appropriate to school-age children.
- As an alternative educational requirement, a director of a school- age program that stands alone may substitute 20 training hours for each required unit of education in Section 10125.1(h)(1). Units and training hours may be combined to meet the total educational requirement.
- In addition to a 3-unit semester administration course, 3 units in early childhood education, child development or school-age courses, the director may substitute 9 core units from the following: recreation, physical education, human services, units earned toward an elementary or middle school teaching credential, early childhood education, child development or school-age child units.
- A director is required to complete 12 units or 240 training hours prior to employment. The remaining 3 units must be completed within one year of employment.
- A director may qualify by possessing an Associate of Arts or a Bachelor’s Degree from an accredited or approved college provided at least 3 units or 60 training hours are in early childhood education, child development, or school-age child courses; and 3 units in administration or staff relations.
- Section 1597.21(f) of the Health and Safety code allows a director to use alternative approved sources of education.
- Verification of education shall be by transcript or certificate with hours completed shown on the certificate.
- A director needs to have verified experience of at least 3 hours a day for a minimum of 100 days in a calendar year. Health and Safety Code Section 1597.21 allows for alternative types of experience.
101516.2 SCHOOL-AGE CHILD CARE CENTER TEACHER QUALIFICATION AND DUTIES
- In addition to Section 101216.1, the following shall apply:
- As an alternative education requirement, a school-age teacher may substitute 20 training hours for each required unit. Units and training hours may be combined to meet the total educational requirements of 12 units or 240 training hours, or any combination thereof.
- School-age teachers may use alternative educational requirements. A teacher may substitute: recreation, physical education, human services, units earned toward an elementary or middle school teaching credential; early childhood education, child development or school-age child units.
- A teacher is required to complete 6 units prior to employment.
- Health and Safety Code, section 1597.21(f), allows a teacher to use alternative approved sources of education.
- Alternative types of experience may also be accepted. To be a fully qualified school-age teacher, experience must be verified showing at least 3 hours a day for a minimum of 50 days in a six- month period.
- In a combination center, a fully qualified teacher shall be designated to work closely with the director planning the daily activities of the school-age center.
101516.5 TEACHER-CHILD RATIO
- In addition to Section 101216.3, the following shall apply:
- One teacher to supervise no more than 14 children.
- One teacher and 1 aide can supervise no more than 28 children.
- Staffing for mixed-aged groups shall be based on the youngest child in the group.
- Directors may be counted in the ratio when actually working with groups of children.
101520 MEDICAL ASSESSMENTS
- Notwithstanding Section 101216.2, the licensee shall not be required to document medical assessments on school-age children who are enrolled in a public or private school.
101520 IMMUNIZATIONS
- Notwithstanding Section 101220.1, the licensee is not required to document immunizations of children also enrolled in a public or private elementary school.
101521 CHILD’S RECORDS
-
101526.1
DAILY INSPECTION FOR ILLNESS
- In addition to Section 101226.1, upon arrival or admittance to the center, school-age children shall be observed for signs of illness. If a child is found to be ill, follow Section 101226.2.
101527 FOOD SERVICE
- In addition to Section 101227, before and after school programs shall offer nutritious snacks to children.
101529.1 SIGN-IN AND SIGN-OUT
-
101538.2
OUTDOOR ACTIVITY SPACE FOR SCHOOL-AGE CHILDREN
- In addition to Section 101238.2:
- Outdoor activity space for school-age children shall by physically separated from space provided other children at the center.
- School-age child care programs that are operated on the site of a functioning school ground are exempt from square-footage requirements.
101538.3 INDOOR ACTIVITY SPACE FOR SCHOOL-AGE CHILDREN
- In addition to Section 101238.3, the following applies:
- Indoor space for school-age children shall be physically separated from space provided other children in the center.
- School-age child care programs that are operated on the site of a functioning school are exempt from square-footage requirements.
101539 FIXTURES, FURNITURE, EQUIPMENT AND SUPPLIES
- In addition to Section 101239, the following applies:
- Toilets used by school-age children shall provide individual privacy. Toilet facilities shall not be used simultaneously by children of both sexes.
- School-age programs that operate on the site of a functioning school are exempt from toilet requirements.
INFANT CARE CENTERS
101351 GENERAL
- Child Care Centers providing infant care shall be governed by the requirements of this subchapter. These centers shall also be governed by the previously listed Child Care Center General Licensing requirements.
101361 LIMITATIONS ON CAPACITY AND AMBULATORY STATUS
A child, whose developmental needs require continuation in an Infant Care Center, may remain in an Infant Care Center up to the age of three years.
101415 INFANT CARE CENTER DIRECTOR QUALIFICATIONS AND DUTIES
- An infant center director must meet the requirements of Section 101215.1, and the following:
- Experience requirements shall be completed in an Infant Care Center or a comparable group child care program with children less than five years of age.
- At least 3 semester units completed must be related to infant care.
- When the infant director is temporarily away from the center, the director shall appoint a substitute director.
- In centers where an assistant director is required, the assistant director shall act as a substitute.
- A fully qualified infant care teacher can act as a substitute for the director, or the assistant director.
- If the director’s absence is more than 30 consecutive days, a substitute director shall meet the qualifications of a director.
101415.1 ASSISTANT INFANT CARE CENTER DIRECTOR QUALIFICATIONS AND DUTIES
- An assistant director shall be present if the center has 25 or more infants in attendance. The assistant director has to be a fully qualified infant teacher and have completed, with passing grades, at least three semester units in administration at an approved college. This course work may be completed within one year of employment of the assistant director.
- The assistant director shall work under the direction of the center director.
101416.2 INFANT CARE TEACHER QUALIFICATION S DUTIES
- In addition to Section 101216.1, infant care teachers need to have taken and passed, at least 3 semesters units in early childhood education or child development, and 3 semester units in the care of infants from an approved college.
- After employment, a teacher who has not completed the 12 required semester units shall complete with passing grades, at least 2 units each semester until the 12 semester units are completed.
- To be a fully qualified infant care teacher, he/she shall:
- Complete 12 semester units, with passing grades, in early childhood education or child development. At least 3 units shall be related to the care of infants.
- Have a least 6 months experience in a licensed infant care program or comparable program for children under five years old.
101416.3 INFANT CARE AIDE QUALIFICATION AND DUTIES
- An aide must work under the supervision of the director or a fully qualified teacher, except when observing sleeping infants.
- Aides shall participate in an on-the job training program.
- An aide shall provide direct care and supervision to infants.
101416.5 STAFF-INFANT RATIO
- There shall be a ratio of one teacher to every four infants.
- An aide may be substituted for a teacher if there is a fully qualified teacher directly supervising no more than 12 infants.
- When in activities away from the center there shall be a minimum of one adult to every two infants.
- The director may be counted in the staff-infant ratio when actually working with infants.
- There shall be one staff visually observing no more than 12 sleeping infants, as long as additional staff are available at the center to meet the above ratios when necessary.
101416.8 STAFFING FOR INFANT WATER ACTIVIT IES
- A ratio of one adult to two infants shall be required during activities near a swimming pool or any body of water.
101417 TODDLER COMPONENT IN AN INFANT CARE CENTER
- Licensees serving infants may create a special program component for children between 18 and 30 months.
- A ratio of one teacher for every 6 toddlers is required.
- An aide participating in on-the job training can substitute for a teacher when directly supervised by a fully qualified teacher.
- Maximum group size is two teachers to 12 toddlers.
- The toddler program shall be conducted in areas physically separate from those used by older or younger children.
101419.2 INFANT NEEDS AND SERVICES PLAN
- A plan must be completed and on file for every infant prior to attending the center. This plan must be signed by the authorized representative.
- The plan shall include: an individual feeding plan, individual toilet training plan, and any services needed different from those provided by the program.
101419.3 MODIFICATIONS TO INFANT NEEDS AND SERVICES PLAN
- The plan shall be updated quarterly or as often as necessary.
101423.1 INFANT CARE DISCIPLINE
- In addition to 101223.3, no infant shall be confined to a crib, high chair, playpen, or any other furniture or equipment as a form of discipline.
101425 INFANT CARE TRANSPORTATION
- Driver has to be 18 years old or older to transport infants.
- The vehicle must contain a first-aid kit.
- Children must be secured in a child passenger restraint system, i.e., a car seat.
- Staff/infant ratios must be maintained whether the vehicle is moving or parked.
- Infants in vehicles shall have constant adult supervision and shall not be left unattended.
101426.2 INFANT CARE ISOLATION FOR ILLNESS
- In addition to 101226.2, the isolation area must have a crib, cot, mat or playpen for each ill infant. This isolation area must be under constant visual supervision by staff.
101427 INFANT CARE FOOD SERVICE
- In addition to 101227, the following shall apply:
- Each infant shall have an individual feeding plan completed prior to the infant’s first day at the center. This plan must be developed by the director, infant’s representative and/or physician.
- The plan shall include: instructions for infant’s special diet, feeding schedule, breast milk or formula, schedule for introduction to solid/new foods, food consistency, likes and dislikes, allergies, schedule for introduction of cups and utensils.
- This plan shall be updated as often as necessary.
- Bottle fed infants shall be fed at least every four hours.
- Infant care centers shall have appropriate food available for the infants.
- The center shall provide only commercially prepared formulas that are stored and prepared in accordance with the label.
- The infant’s representative may provide formula or breast/mother’s milk. Such formula or milk shall be bottled before being accepted by the center.
- Bottles shall be labeled.
- Center may heat formula or breast/mother’s milk.
- Center must keep a supply of nipples. Bottles/nipples can not be shared between infants unless sterilized.
- Infants unable to hold a bottle shall be held by staff for bottle feeding.
- Bottles cannot be propped; infants shall not carry a bottle while ambulatory; a bottle given to an infant able to hold his/her own shall be unbreakable.
- High chairs or appropriate seating equipment shall be used for infants during feeding. Infants unable to sit unassisted shall be held by staff for feeding.
- Bottles, dishes and food containers brought from infant’s home shall be labeled with infant’s name and current date.
- Formula partially consumed in a bottle shall be discarded at end of each day.
- Food shall be discarded if not consumed within 72 hours of date on the container label.
- The infant care center shall not serve honey.
- Commercially prepared baby food in jars shall be transferred to a dish before being fed to the infant. Any food left over in the dish at the end of a meal shall be discarded.
- Mother may make arrangements with center for privacy to nurse infant.
- Bottles and nipples in center shall be sterilized.
- Infants shall not be bathed in, and diapers or clothing shall not be rinsed in, the food preparation area.
101428 INFANT CARE PERSONAL SERVICES
- There shall be a written toilet-training plan for each infant being toilet trained.
- Whenever a potty chair is used, it shall be placed on the floor and promptly emptied, cleaned and disinfected after each use.
- No child shall be left unattended while on a potty chair or seat.
- Each child shall receive instruction and assistance in handwashing after use of the toilet. The infant shall be kept clean and dry at all times.
- Soiled or wet clothing provided by the infant’s representative shall be placed in an airtight container and given to the representative at the end of the day.
- When changing an infant’s diaper, each infant shall be on a changing table and no infant shall be left unattended while on the changing table.
- Towels and washcloths used for cleaning infants shall not be shared and shall be washed after each us.
- The changing table shall be disinfected after each use.
101429 RESPONSIBILITY FOR PROVIDING CARE AND SUPERVISION FOR INFANTS
- In addition to 101229, each child shall be constantly supervised and under direct visual observation by a staff person at all times. Under no circumstances shall any infant be left unattended.
101430 INFANT CARE ACTIVITIES
- The center shall implement a written plan to ensure the provision of indoor and outdoor activities designed to meet the needs of the infants, including but not limited to, quiet and active play; rest and relaxation; eating; toileting; individual attention; being held by a caregiver.
- All infants shall be given the opportunity to nap/sleep without distraction or disturbances.
- No infant shall be forced to sleep, stay awake, or stay in the napping area.
101438.1 INFANT CARE GENERAL SANITATION
- All items used by pets and animals shall be kept out of the reach of infants.
- Each caregiver shall wash his/her hands with soap and water before feeding and after each diaper change.
- Areas that infants have access to shall be washed, cleared and sanitized as follows: floors shall be vacuumed or swept and mopped daily and as often as necessary. Carpeted floors shall be vacuumed daily and cleaned at least every 6 months. Walls shall be washed with disinfecting solution at least weekly.
- The diaper changing area shall be disinfected including walls and floors. After each diaper change, counter tops, sinks, drawers and cabinets near diaper changing area shall be washed.
- Objects that are used by infants that are mouthed shall be washed and disinfected.
- All disinfectants and other hazardous materials shall be stored inaccessible to infants.
- Only dispenser soap in an appropriate dispenser shall be used.
- Only disposable paper towels in an appropriate holder or dispenser shall be used for hand drying.
101438.2 OUTDOOR ACTIVITY SPACE FOR INFANTS
- In addition to Section 101238.2, the following shall apply:
- Outdoor space shall be physically separated from space used by children not in the infant center.
- Outdoor space shall be equipped with age-appropriate toys and equipment
101438.3 INDOOR ACTIVITY SPACE FOR INFANTS
- The sleeping area for infants shall be physically separated from the indoor activity space.
- The indoor activity space shall be equipped with age- appropriate washable toys and equipment.
101439 INFANT CARE CENTER FIXTURES, EQU IPMENT, AND SUPPLIES
- In addition to Section 101239, the following shall apply:
- There shall be appropriate furniture and equipment such as cribs, cots or mats, changing tables and feeding chairs.
- High chairs or low-wheeled feeding tables or any equipment used for seating an infant shall have broad-base legs.
- No infant shall be permitted to stand up in a high chair.
- All equipment shall be washed/disinfected after each use.
- Infant changing tables shall have a padded surface no less than 1 inch thick; raised sides at least 3 inches high; kept in good repair, within an arm’s reach of a sink and not located in the kitchen or food preparation area.
- There shall be one hand washing sink for every 15 infants and one potty chair for every 5 infants being toilet trained.
- Infants shall not be permitted to play with the potty chair.
- Toy storage containers shall be safe and maintained in good condition.
- Containers shall not be lockable.
- Toys shall be safe and not have any sharp edges, or small parts.
- Fixtures, furniture, equipment or supplies shall not be made of or contain toxic substances.
101439.1 INFANT CARE CENTER NAPPING EQUIPMENT
- In addition to Section 101239.1, the following shall apply:
- A standard size six-year crib or porta-crib shall be provided for each infant who is unable to climb out of a crib.
- Cribs shall not limit the ability of staff to see the infant.
- Cribs shall not limit the infant’s ability to stand upright.
- Crib mattresses shall be covered with vinyl or similar moisture- resistant material; shall be wiped and disinfected daily and when wet or soiled.
- Cribs shall be maintained in a safe condition.
- Each crib shall be occupied by only one infant at a time.
- Each infant’s bedding shall be used by him/her only, and replaced when wet or soiled.
- Bedding shall be changed daily or more often if required.
- Cribs, mats or cots shall be arranged so as to provide a walkway and work space between the cribs, mats or cots sufficient to permit staff to reach each infant without stepping over any other infant.


1.8: Why It Matters- Introduction to Management
Why learn about management?
Before the heyday of Apple iPhones, Nokia dominated the mobile phone market. Would it surprise you to know that Nokia began in 1871 in Finland as a paper mill company? Later, it diversified into making rubber tires and boots, laid cables, and eventually moved into making emergency radiophones and commercial car phones. Over the course of its evolution, Nokia’s top managers stayed focused on the external business environment and were willing to make the hard decisions—regardless of how risky or uncertain they seemed at the time—to stay competitive, even if it meant the organization had to change industries and retrain its workforce. [1]
That management focus is even more essential today. ThyssenKrupp AG, a major steel manufacturer in Germany, is responding to competitive market challenges created by cheap Chinese steel by reducing its steel production. Instead, it is fast becoming the leader in manufacturing next-generation elevators—once a sideline and now the company’s profit-driver. [2] ThyssenKrupp is facing issues similar to those addressed by Nokia a century earlier.
How do organizations survive in a world where conditions are constantly changing? Who makes the difficult decisions that result in the success or failure of the organization? Is making good business choices an art or a science? The study of management answers these kinds of questions. To think of managers as people hunkered down in offices handling routine decisions is to miss the most important and dynamic aspect of management. Managers enable businesses to adapt and thrive in today’s competitive global markets.
As you read, keep this example of Nokia and ThyssenKrupp and other businesses that you may know in mind.
- Satpathy, S. (2014, April 26). A brief history of Nokia: From a paper mill, to the world's biggest mobile company to being acquired by Microsoft | Latest Tech News, Video & Photo Reviews at BGR India. Retrieved July 28, 2017, from http://www.bgr.in/news/a-brief-history-of-nokia-from-a-paper-mill-to-the-worlds-biggest-mobile-company-to-being-acquired-by-microsoft/ ↵
- Andresen, Tino. "Germany's Biggest Steelmaker Set to Unveil a Future Beyond Steel." Bloomberg.com. June 19, 2017. Accessed July 28, 2017. https://www.bloomberg.com/news/articles/2017-06-19/germany-s-biggest-steelmaker-set-to-unveil-a-future-beyond-steel . ↵
Contributors and Attributions
- Why It Matters: Introduction to Management. Authored by : Lynn Bruton. Published by Lumen Learning. License : CC BY: Attribution
- Image: Nokia evolucion tamano. . Authored by : Jorge Barrios. Located at : https://commons.wikimedia.org/wiki/File:Nokia_evolucion_tama%C3%B1o.jpg . License : Public Domain: No Known Copyright