# Math 116 - Chapter 4 & 7 Study Guide

1. Simplify the expressions involving logarithmic and exponential functions. Give exact values. For example log4 41.7 = 1.7. Twelve parts.
2. Identify the conic section or degenerate case. Choices are no graph, point, line, parallel lines, intersecting lines, parabola, circle, ellipse, and hyperbola. Nine parts.
3. Write the equation of the conic section. Three parts.
4. Write the expression as a sum, difference, and/or constant multiple of logarithms and simplify (if possible). Three parts.
5. Write the expression as the logarithm of a single quantity. Three parts.
6. Solve the equations. Give an exact answer (example, leave answer as ln 7 rather than going to the calculator to get a decimal approximation). Pay attention to domain. Four parts.
7. Given a parametrically defined curve, complete a table of values and sketch the curve, indicating the direction of increasing t. Eliminate the parameter and solve for y. Be sure to include any restrictions that are necessary.
8. Given the equation of a parabola, find the vertex, focus, and directrix. Sketch the graph.
9. Given the equation of an ellipse, find the center, foci, and vertices. Sketch the graph.
10. Given the equation of a hyperbola, find the center, foci, vertices, and asymptotes. Sketch the graph.
11. Write the equation of the conic section in standard form. This will involve completing the square. Three parts.
12. Identify the translation and give the domain and range of the translated graph.
13. Analyze a polynomial function.
14. Analyze a rational function.
15. Write the equation of the graphed relation. Nine parts.

## Notes

• Questions 1 - 3 are to be done without a calculator. You may use a calculator for the rest of the exam.
• None of the problems on the test are straight from the text, but should be similar to the problems in the text.
• There is a take-home portion of the exam worth 38 points and is due the day of the exam.