Fall 1998, Math 100
CHAPTER 1

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

Due 9/4 at 8am, assigned 9/2

Suggestions for Reading a Math Book
Course Policies
Section 1.1 Functions All Around Us

• To read: all of course policies, syllabus, suggestions, and Section 1.1.
• Be sure to understand: The definition of a function, and all the associated examples (the graph of metabolic rate and the following discussion, the postage example).
2. When is the first exam in this class?
3. Under what conditions do I give make-up exams?
On a more serious note (but you should answer the above, just so YOU know)
4. What are the different ways functions can be given?
5. Think about the temperature (at Wheaton, on September 3) and the time of day. It seems clear, to me at least, that there is a relationship between these two.

Would you say that the temperature is a function of the time of day, or that the time of day is a function of the temperature?

Due 9/7 at 8am, assigned 9/4

Guidelines for Homework Presentation
Section 1.2 Describing the Behavior of Functions

• To read: pages 9-bottom of page 12
• Be sure to understand: what it means for a function to be increasing, decreasing, concave up, and concave down; what turning points and inflection points are; the example on page 12.
Look at the figure 1.22 on page 23. This graph shows the height h of a ball t seconds after it was tossed upward.
1. Between what times is the height function h increasing? Between what times is the height function h decreasing?
2. Between what times is the height function h concave up? Between what times is it concave down?

Due 9/9 at 8am, assigned 9/7

Suggestions for Reading a Math Book
Section 1.2 Describing the Behavior of Functions
Section 1.3 Representing Functions Symbolically

• To read: Section 1.2 pages 12-13, Section 1.3 pages 16-bottom of page 17.
• Be sure to understand: periodic functions, independent and dependent variables;
1. Give an example of a real-life process which is periodic (beyond those mentioned in the book.)
2. The weight of a package is related to the number of stamps needed to mail it.
1. Does the weight depend on the number of stamps, or does the number of stamps depend on the weight?
2. Is this a function? (Of course, refer back to the definition of a function, which you can find by flipping pages, or, more efficiently, by using the index!)
3. Which variable is dependent? Which is independent?
3. My son Kenny just loves peanut butter, tuna, and mustard on crackers. Assuming I always put 1 tbsp of tuna on (with 3 grams of protein), then the protein he gets will vary only with how much peanut butter I put on. Let's just say that the protein he gets with one such cracker (P) will depend on the amount of peanut butter (pb) as follows:
P(pb)=3+2pb.
How many grams of protein does he get if I put
1. no peanut butter on the cracker (pb=0)?
2. 1 tbsp of peanut butter on the cracker (pb=1)?

Due 9/11 at 8am, assigned 9/9

Section 1.3 Representing Functions Symbolically

• To read: bottom of p.17-p.19
• Be sure to understand: why a person's phone number is not a function of who the person is; the definition of domain and range.
1. Is the time of high tide a function of the day of the year? (To avoid confusion, restrict yourselves to considering only one year.)
2. Consider the function
g(x)=1+(1/x).

1. What is g(2)?
2. Is 0 in the domain? (As usual, explain).
3. Is 0 in the range?

Due 9/14 at 8am, assigned 9/11

Section 1.4 Connecting the Geometric and Symbolic Representations
Section 1.5 Mathematical Models

• To read: all of Sections 1.4 and 1.5
• Remember: Gateway exam on Thursday
• Be sure to understand:I will not be covering axes, ordered pairs, and how to plot points in class, so be sure you really understand those thoroughly (or come talk to me.) Also pay close attention to determining whether a curve is a function, and if it is, how to determine the domain and range.
1. Find where the function
f(x)=x2+4
crosses the vertical axis.
2. Consider the tossed ball whose height as a function of time is given on page 22, and which we see graphed in Figure 1.22 on page 23.
1. Is the point (3.3,40) on the curve shown in Figure 1.22?
Hint:Should you figure this out by looking at the graph, or might there be a better way?
2. For this same function, f(4)=0. What does this have to do with the graph? What does it have to do with the ball?
3. Must a mathematical model describe all aspects of the process it represents?
4. What is the difference between interpolation and extrapolation?
Here ends Chapter 1
Go to Chapter 2!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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