# Math 116 - Chapter 1 Study Guide

1. Consider the graph of the function y=f(x) with the given domain and range. In each case identify the translation in English and give the domain and range of the translated function. Five parts.
2. Find the equation of the line that passes through the given point with the given slope. Look at problems 1.2.33-42.
3. The graph of a relation is given. Indicate whether or not the graph is the graph of a function and also any symmetries about the x-axis, y-axis, or origin. Four parts. Look at problems 1.4.13-18 and 1.4.19-22b.
4. Find the equation of the line that passes through the two given points. Look at problems 1.2.43-52.
5. Determine if the equation represents y as a function of x. Three parts. Look at problems 1.3.13-24.
6. Given a function, evaluate it at the specified values and simplify. Three parts. Look at problems 1.3.27-38.
7. Given two functions f and g, find f composed with g and g composed with f. Two parts. Be sure to state any restrictions that are necessary. Look at problems 1.6.39-44.
8. Given a function h, decompose it into two functions f and g. Two parts. Look at problems 1.6.57-64.
9. Given a function, find its domain. Three parts. Look at problems 1.3.57-70.
10. Given a function, find and simplify the difference quotient at a specific point. The difference quotient is given to you on the exam, you just need to be able to simplify it. After simplifying, evaluate the difference quotient at a series of points (use the table mode on your calculator if you wish). Look at problems 1.3.79-86 and 1.6.71-78.
11. Given a table of values for x, f(x), and g(x), find the combination, composition, and inverse of functions. See example at bottom of this page. Eight parts.
12. The graph of a relation is given. Sketch the graph of the inverse of the relation on the same coordinate system as the original graph. Look at problems 1.7.73-74.
13. Determine the intervals where the function is increasing, decreasing, and constant. Look at problems 1.4.19-22.
14. Find the inverse of a function. Look at problems 1.7.43-54.
15. Know the equations and graphs of the basic functions. Constant, Linear (identity), Quadratic (squaring), Cubic, Square Root, Absolute Value, and the Greatest Integer Function. Identify the common function and the transformation of the graph; also write the formula for the graphed function. Look at problems 1.5.15-26.

## Notes:

• There is a one-to-one correspondence between problems on the study guide and problems on the exam. In other words, #13 on the study guide is what problem #13 on the exam will be about.
• There is a 25 point take home portion of this exam. The answers to the some of the material on the take home exam can be found using material in the lecture notes on the Internet. The take home portion is due the day of the regular exam.
• The in-class portion of the exam will be worth 75 points.

#### Example for #11

x 1 2 3
f(x) -1 5 1
g(x) 3 1 -1
• Find f(3): Find x=3 in the first row, then go down that column to the f(x) row to get f(3)=1.
• Find f composed with g of 2. That is f [ g(2) ]. Since g(2)=1, we then find f (1), which is the final answer, -1.
• Find f -1(5). That's the x value where f(x)=5, so find 5 in the f(x) row and then read the x value. Since f(2)=5, then f -1(5)=2 and the answer is 2.

## Point values for each question.

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 10 3 8 3 3 3 6 4 6 5 7 2 3 2 10 75