Math 116 - Chapter 1 Study Guide

1. Consider the given function with the indicated domain and range. In each case identify the translation in English and give the domain and range of the translated function. Eight parts.
2. Use a graphing utility to graph the function. Describe the viewing window. Look at problems 1.1.59 - 1.1.62.
3. Find three additional points on the line passing through the given point with the given slope. Look at problems 1.2.17 - 1.2.25.
4. Find the equation of the line that passes through the given point with the given slope. Look at problems 1.2.51 - 1.2.59.
5. Determine if the equation represents y as a function of x. Three parts. Look at problems 1.3.13 - 1.3.22.
6. Evaluate the function at the specified value of the independent variable and simplify. Three parts. Look at problems 1.3.25 - 1.3.35.
7. Find the composition of functions. Two parts. Look at problems 1.6.35 - 1.6.43.
8. Find the domain of the function. Three parts. Look at problems 1.3.51 - 1.3.60.
9. Write the equation of each of the six basic graphs from the front cover of the textbook and sketch its graph.
10. Find an equation for the line passing through the given points. Look at problems 1.2.41 - 1.2.49.
11. Find the difference quotient for the given function, and simplify. You are responsible for knowing the formula for the difference quotient. Look at problems 1.6.61 - 1.6.64.
12. Sketch the inverse of the given relation. A relation is sketched, you need to sketch its inverse. You are not given the equation of the relation, just the graph. Look at problems 1.7.1 - 1.7.4.
13. Determine whether the function is one-to-one. If it is, find the its inverse. Three parts. Look at problems 1.7.41 - 1.7.59. Pay special attention to those that require restrictions.

Notes:

• None of the problems are straight from the text, but are very similar to problems in the text with either a few numbers or signs changed.
• The notation 1.1.19 - 1.1.25 means look at problems 19 - 25 in section 1.1
• 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.
• Whenever a box appears on the test, you should make a sketch from the graphing calculator in that box. You should NOT automatically use the Standard Setting. Fit the interesting portions of the graph into the viewing window so the graph takes a substantial portion of the screen and (usually) contains the x and y-axes (although not necessarily in the middle) and then draw the graph. Describe your viewing window (Xmin, Xmax, Ymin, Ymax).
• 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.