## Math 116: Chapter 5 Study Guide

1. Sketch the graph of the rational functions. Three parts. Things that will be checked are the correct behavior at x-intercepts and vertical asymptotes, and the horizontal asymptote (or lack thereof). (12 points total).
2. Write a rational function which exhibits the given characteristics. There will be vertical asymptotes, x-intercepts, a horizontal asymptote, and a hole in the graph. The vertical asymptotes will be both in the same direction and in different directions. The x-intercepts will cross and touch. (4 points).
3. Write the partial fraction decomposition for the rational expressions. Two parts. (8 points).
4. Identify the conic section or degenerate case. There are nine choices, each is used once. The choices, in alphabetical order are: circle, ellipse, hyperbola, intersecting lines, line, no graph, parabola, parallel lines, and point. (4 points).
5. Modeling problem. Look at problems 5.1.65 - 5.1.68, and review problems 23 - 26. (5 points).
6. Modeling problem. The lengths of the major axis and minor axis of an ellipse are given. Find the equation of the ellipse. (5 points).
7. Sketch the graph of the conic sections. Three parts. One parabola, one ellipse, one hyperboa (not necessarily in that order). You will have to complete the square to put it into standard form for one of these. (12 points).

### Notes:

• The in-class portion of this exam is 50 points.
• The take-home portion of the exam is 50 points. The take-home portion will not be available on the web.