Fall 1997, Math 100
CHAPTER 1

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

### 9/3, respond by 5pm 9/4

Suggestions for Reading a Math Book
Course Policies

### Section 1.1 Functions All Around Us

• Be sure to understand: Page 2 thru the middle of page 3.
1. What are the different ways functions can be given?
2. What is the life expectancy of a child born in 1960?
3. Why is the time needed for a trans am to accelerate a function of the final speed?
4. In the trans am example, why do we put the final speed on the horizontal axis and the time on the vertical axis?

### 9/5, respond by 5pm 9/7

Guidelines for Homework Presentation

### Section 1.2 Describing the Behavior of Functions

• 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.
1. Why is the function that describes the world's population an increasing function?
2. Give a real-world example of a function which is decreasing and concave up.
3. If you are asked to identify where a function is increasing, would your answer be an interval (a region of points) or a specific point?

### 9/8, respond by 5pm 9/9

Suggestions for Reading a Math Book

### Section 1.3 Representing Functions Symbolically

• Be sure to understand: independent and dependent variables;
1. Consider the function y=f(x)=x2.
1. What does this function do to any real number (in words)?
2. What is the domain of this function?
3. What is the range of this function?
2. The amount of postage on a package is related to how much the package weighs.
1. Would you say postage is a function of weight, or weight is a function of postage?
2. The two things which vary, and hence the two variables, are the amount of postage and the weight. Which is the dependent variable, and which is the independent variable?

### Section 1.4 Connecting the Geometric and Symbolic Representations

• Be sure to understand: Examples 1 through 4
1. Is the point (3.3, 40) on curve shown in Figure 1.22?
2. What are the domain and range of the function discussed on page 22 and shown in Figure 1.22?
3. Does the graph in figure 1.22 represent the path the ball travels?
4. Why is it true that if a vertical line crosses a curve more than once, then that curve cannot possibly represent a function?

### Section 1.5 Mathematical Models

1. Must a mathematical model describe all aspects of the process it represents?
2. Briefly list the steps involved in using mathematics to describe the real world.
3. What is the difference between interpolation and extrapolation?

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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