## Math 116: Study Guide - Chapter 3

1. Find the equation of the perpendicular bisector of the line segment between two points. See the take home problem on finding the equation of the circle passing through the three points. This is broken down into four parts to help you and test your ability to perform specific parts of the problem. First find the midpoint, then the slope of the line and the slope of the perpendicular line. Finally, find the equation of the perpendicular bisector.
2. Give the translation, and the domain and range of the translated function. Six parts. Look in your notes at the many quizzes we had on this material.
3. Find the x-intercept(s), y-intercept(s) and test for symmetry about the y-axis, x-axis, and origin. An example has been worked for you. Three parts. Look at problems 39 - 58 in section 3.2. On the intercepts, you need only give the abscissa or the ordinate, you do not need to give the full ordered pair.
4. Find the domain of a function. Three parts. Look at problems 29 - 38 in section 3.4.
5. Find the difference quotient for the given function. Look at problems 47 - 52 in section 3.4, but concentrate on difference quotients like 49 and 50. The one on the test will be of the form [ f(x+h) - f(x) ] / h, but the function is not one of the ones given. The formula for the difference quotient is given on the exam.
6. Evaluate the indicated function for two given functions. Three parts. Look at problems 9 - 20 in section 3.6.
7. Find the composition of two functions. Two parts. Look at problems 25 - 32 in section 3.6.
8. Determine if a function is one-to-one. If the function is one-to-one, then find the inverse of the function. Two parts. Look at problems 37 - 52 in section 3.7.
9. Variation problem. Look at problems 41 - 49 in section 3.8*. Be sure to write the mathematical model used.
10. Sketch some graphs. Four parts. Look at the graphs of the functions on page 208, realize that some translation has been done to each of them. Also, know how to sketch a circle.

### Notes

* - problem is directly from text.