## 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. Eight parts.
2. 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. Three parts.
3. Find the equation of the line that passes through the given point with the given slope.
4. Find the equation of the line that passes through the two given points.
5. Determine if the equation represents y as a function of x. Three parts.
6. Given a function, evaluate it at the specified values and simplify. Three parts.
7. Given two functions f and g, find f composed with g and g composed with f.
8. Given a function h, decompose it into two functions f and g.
9. Given a function, find its domain. Three parts.
10. Given a function, find and simplify the difference quotient. The difference quotient is not given on the exam, you need to know it.
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 page. Eight parts.
12. Know the equations and graphs of the six basic graphs from the front cover of the textbook.
13. 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.

### 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

 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. x 1 2 3 f(x) -1 5 1 g(x) 3 1 -1

Point values for each question.

 # 1 2 3 4 5 6 7 8 9 10 11 12 13 Total Pts 16 6 3 3 3 6 6 4 6 5 8 6 3 75