Fall 1999, Math 101

CHAPTER 1

Be sure to check back often, because assignments may change!

Due Friday 9/10 at 9am

• Pay attention to: all of it: I tried to address as many issues as I could think of. Any questions? Ask me!
• Reminder: Keep this in your folder.

• Pay attention to: exam dates, especially first gateway. Project due dates.
• Reminder: enter these dates in your calendar now.

Section 1.1: Functions, Calculus Style

• To read: Through Example 6
• Be sure to understand: Examples 5 and 6

E-mail Subject Line: Math 101 Your Name 9/10

1. Give an example of a function that is defined by words, without an explicit formula.
2. Using the function m(x) in Example 4, what is m(-2)?
3. Is the balloon in Example 5 rising or falling at t=3 minutes?
4. Is the upward velocity positive or negative at t=3 minutes?

Reminders:

• Explain, briefly, how you arrive at each of your results.
• Come to lab at 1pm Thursday.
• Find out this week's problem set assignment, listed at the bottom of this course's web page. While it's not due until Friday, treat it as if it's due Wednesday (every week). Come to my office hours with quetions, bring remaining questions to class Wednesday. The time between Wednesday and Friday is intended only for writing the solutions in a clear and concise way that explains your thought processes.

Unfortunately, I can not respond individually to the reading assignments every day. I will, of course, respond to direct questions. There does not appear to be an easy way for me to automatically send you a "message received" note. Usually e-mail goes through fine, but sometimes messages do disappear without bouncing back to you. To be on the safe side, send yourself a copy every time you send me a response. Every now and then, ask me if there are any missing assignments, and if there are, forward your (dated) copy.

Due Monday 9/13 at 9am

Section 1.2: Graphs

• Be sure to understand: Examples 3 and 4, New Functions From Old

E-mail Subject Line: Math 101 Your Name 9/13

1. Explain why the graph of x2+y2=1 (seen in Example 1) can not be the graph of a function.
2. Exactly how far above the x-axis is the curve shown in Example 2 at x=3?
3. In Example 3, the authors say that f(1) is approximately -6, but that we'd need more information to know whether f(1)=-6 exactly. What kind of information could tell us whether f(1)=-6?
4. How does the graph of f(x)+2 compare with the graph of f(x)? The graph of 2f(x) compare to f(x)? (Here f is some random function).

Reminder:

Be working on your first problem set. While it's not due until It's a group set, so start paying attention to who you want to work with. You may not want to base your decision on who you are (or would like to be) buddies with, but instead on who you always switch later.)

Due Wednesday 9/15 at 9am

Section 1.3: Machine Graphics

• Be sure to understand:The six views of the Sine function; Examples 1 and 2

Section 1.4:

• Be sure to understand:The definition of a function, the Five Examples, the definitions of domain and range, the reprised definition of a function, Periodic Functions: the Symbolic View.

E-mail Subject Line: Math 101 Your Name 9/15

1. Calculate h(.5), where h is the third of the five examples.
2. Let g(t)= the world's human population t years C.E. Give the domain and range of g.
3. Find the domain and range of m(x)=x2.
4. How can you recognize a periodic function from its graph?

Reminder:

• Bring unresolved questions on the first problem set to class Wednesday.
• We now have a Calc assistant, Annie MacHaffie. She'll be in lab on Thursday to be introduced, and she'll be available Thursday evenings at 8:30. If you'd like to meet with her to ask her questions, e-mail her by 5pm Thursday at amachaff.

Due Friday 9/17 at 9am

re-read: course policies ( make sure all is clear & you're comfortable)
Section 1.5 A Field Guide to Elementary Functions

• To read: up to Trig Functions (page 61)
• Be sure to understand: The definitions of exponential and logarithmic functions, the relationship between all graphs of exponential functions, the relationship between all graphs of logarithmic functions, the common points of each, and the relationship between the graph of a function bx and logbx.

E-mail Subject Line: Math 101 Your Name 9/17

1. What is the domain of the rational function x2/(x2-1) in Example 3? What is the relationship between the domain and the asymptotes?
2. Is ey an exponential function? How about (Pi)x? Why or why not?
3. If you were shown the graph of a monotonically increasing function, what would you look for to decide whether it could be an exponential function, or to eliminate that possibility?
4. What logarithm function corresponds to the exponential function 3x?

Reminder:

• PS 1 is due Friday. Your group should turn in a joint version. Photocopy it now (and again when you get it back from the grader), so that you each have a copy. Remember to note on it who the "recorder" was--the person who did the writing. (A star by that person's name will suffice). Next time, switch recorders.

Due Monday 9/20 at 9am

Section 1.5 A Field Guide to Elementary Functions (continued)

• Be sure to understand: The sine and cosine functions defined as circular functions; every point on the unit circle corresponds to a value of both the sine and the cosine functions.

E-mail Subject Line: Math 101 Your Name 9/20

1. Can sin(x)=2 for some value of x? Why or why not? What are the domain and range of sin(x)?
2. Explain, in more detail than the book does, why sine and cosine are each 2 Pi periodic.
3. Evaluate sin2(38)+cos2(38) without a calculator.

Reminders:

• Look at PS 2 on the course web page. This is an individual problem set. While you're welcome and encouraged to consult with your colleagues, you must not only work on every part of this problem set (as you must on group sets as well), but use your own words in describing the solutions as well.

Due Wednesday 9/22 at 9am

Section 1.6: New Functions from Old

• To read: Through Example 4
• Be sure to understand: The definition of the composition of two functions, the examples that shows that order matters.

E-mail Subject Line: Math 101 Your Name 9/22

1. Using f and g in Example 2, what is (g o f)(2)?
2. Let f(x)=x3 and g(x)=sin(x).
• What is (f o g)(x)?
• What is (g o f )(x)?

Reminders:

• Bring questions on PS 2 to class on Wednesday.
• If after class you still have questions, come to office hours or e-mail Annie and arrange to meet her at 8:30 in A102 on Thursday evening.

Due Friday 9/24 at 9am

Project 1: Read before lab Thursday
No reading assignment from text for Friday! Enjoy

Oops! Yes there is!

Read through the Guide to Writing in Mathematics Classes<\u> that I hand out in lab Thursday. Note:

• Friday we'll either be working on the project (especially if we have/had to spend Thursday catching up) or doing some other in-class work to cement the ideas of Chapter 1.

Here ends Chapter 1
Go to Chapter 2!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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