Fall 1997, Math 100
Chapter 2

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

### 9/15, respond by 5pm 9/16

Guidelines for Homework Presentation

### Section 2.1 Introduction Section 2.2 Linear Functions

• Be sure to understand: "The Graph of a Linear Function" (pages 42-43); Example 1.
1. When do we use linear functions to model a relationship?
2. If you're trying to find the equation of a line through two data points, is it easiest to use the point-slope form or the slope-intercept form?
3. In Example 2, at what rate do the chirps per minute increase as the temperature increases?

### Section 2.2 Linear Functions

1. In Example 3, how did the authors find the equation
S=f(t)=88+2.17t?

2. In Example 4, if the authors had used the point (60,70) instead of the point (20,90), would they have gotten a different linear equation? (Try it!)
3. What does the sign of the slope tell us about a line?

### Section 2.2 Linear Functions

1. At what rate does the chirping of teh striped cricket seem to increase as the temperature increases?
2. Write the equation of a line perpendicular to
y=(5/4)x-7.

### Section 2.3 Exponential Functions

• Be sure to understand: Why saying the population is growing by a factor of 1.029 means the same thing as saying the population is growing by 2.9%. Example 2.
1. For what types of situations might we consider using an exponential function as the model?
2. Predict the world's population in 152 years.

### 9/24, respond by 5pm 9/25

Suggestions for Reading a Math Book

### Section 2.3 Exponential Functions

• To read: Bottom of page 64-Page 68
• Be sure to understand: Example 3; the distinction between "where...?" and "what is...?" on page 66; Example 4.
1. Suppose we are faced with data reflecting a functional relationship. What do we look at to determine if the function is linear? How about exponential?
2. Simplify [12k^2 * (h^3)^5 ]/[4k^3 * h^6 ] using the rules for exponents.

### Section 2.4 Power Functions

• To read: Page 74-middle of page 77
• Be sure to understand: pages 76-77
1. What is the difference between a power function and an exponential function?
2. Describe the symmetry of even and odd power functions.
3. What happens to any number between 0 and 1 if you raise it a higher and higher power? (For instance, consider .1, (.1)^2, (.1)^3, (.1)^4, etc.)
4. What happens to any number greater than 1, if you raise it to a higher and higher power? (For instance, consider 5, 5^2, 5^3, 5^4, etc.)

### Section 2.4 Power Functions

• Be sure to understand: fractional powers;negative powers; the behavior patterns of the power functions.
1. Which wins the race to infinity, x^3 or x^15?
2. Which wins the race to zero, x^3 or x^15?
3. Write the instructions "first take the fourth root of z and then raise the result to the 7th power" in mathematical notation.
4. What happens to any number greater than 1, if you raise it to a higher and higher power? (For instance, consider 5, 5^2, 5^3, 5^4, etc.)

### Section 2.5 Logarithmic Functions

• To read: Page 85-middle of page 91
• Be sure to understand: Behavior of the log function; the logarithm properties.
1. Why do we use need logarithms?
2. In discussing the population of Florida, why does knowing that the function is always increasing tell us that there must be exactly one value of t for which the population (P) is 20?
3. Why is log(1)=0?
4. Solve for x is the equation (9/5)^x=100

### Guidelines to Writing a Mathematics Paper Project 1

• Be sure to understand: All
None, but start thinking about how to approach the project.

### Section 2.5 Logarithmic Functions

• To read: Middle of page 91-Page 96
• Be sure to understand: Changing Bases
1. What is the difference between solving an equation numerically (or graphically), and solving algebraically?
2. How much stronger is a magnitude 6 earthquake than a magnitude 3 earthquake?

### Section 2.6 Comparing Rates of Growth

• Be sure to understand: Table on page 100-101.
1. Name a function which grows faster than f(x)=x^5000.
2. Name a function which grows slower than f(x)=x^(.0001).

### Section 2.6 Comparing Rates of Growth

• To read: re-read all of Section 2.6. Also re-read all of the Guidelines to Writing a Math Paper, and re-read the checklist.
• Be sure to understand: all
1. Which grows faster as x increases, 5^x or 10^x?
2. Is x^(1/4) increasing or decreasing? Concave up or concave down?
3. Which decays faster, x^(-10) or 10^(-x)?
4. Which grows more slowly, x^(1/1000) or log(x)?
• E-mail subject line: Math 100 Your Name 10/17
• Begin studying for the exam: See the suggestions for 10/20.

### Study for Exam!

• To read: Chapters 1 & 2
• Be sure to understand: Everything
• Study Suggestions:
1. Do not put off studying for this exam until the day before. Begin at least the week-end before!
3. Read the chapter summaries at the end of both chapters.
4. Make lists of the main points of each section. Think about why we care about each of those topics and how they're all related.
5. Do the problems on the study guide.
6. Do the review problems at the end of each chapter.
7. Look over all your homework, and redo as many of them as you have time for.
8. Come look at, or better yet photocopy, my solutions to the homework problems. Use them as yet another study guide.
9. Look for the big picture, and for patterns. How are the various topics similar? How are they different? Were there some ideas that showed up over and over again? Did we do the same process repeatedly?

### Section 2.7 Inverse Functions

• Be sure to understand: The relationship between the graph of a function and its inverse. The two graphical methods for determining whether a function has an inverse.
1. (a) Convert 60 degrees Fahrenheit to degrees Celsius.
2. Let f(x)=x^3. Then the authors claim that the inverse function is the cube root of x.
(a) Calculate f(5).
In other words, plug your answer to (a) into the inverse function.
In still other words, evaluate f^(-1)(f(5)).
3. Use your answers to (1) and (2) to explain what the authors mean by saying that a function and its inverse undo each other.
4. Why do we care about inverse functions? When do we use them?
• E-mail subject line: Math 100 Your Name 10/22

Here Endeth Chapter 2
Now we move on to Chapter 4

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

Back to: Precalculus | My Homepage | Math and CS