# Study Guide: Chapter 5

## Math 116

- 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). (24 points total).
- 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. (9 points).
- Write the partial fraction decomposition for the rational expressions. Two parts. (12 points).
- 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. (9 points).
- Find the equation for the specified conic sections. Three parts; one parabola, one ellipse, and
one hyperbola. Look at problems 5.4.15 - 5.4.18; 5.4.29, 5.4.33; 5.4.47 - 5.4.50. (18
points).
- Modeling problem. Look at problems 5.1.65 - 5.1.68, and review problems 23 - 26. (5
points).
- Modeling problem. The lengths of the major axis and minor axis of an ellipse are given. Find
the equation of the ellipse. (5 points).
- 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. (18 points).