# Math 116 - Chapter 4 & 7 Study Guide

No Calculators are allowed on this exam.

1. Find the inverse of the function. Look at problems 1.7.53-62.
2. Rewrite the exponential expression in logarithmic form. Look at problems 4.2.9-16.
3. Rewrite the logarithmic expression in exponential form. Look at problems 4.2.1-8.
4. Find the greatest integer of a logarithmic expression. In English, that means to give the integer part (usually first digit) of a logarithm. For example, the log5.4 412 is somewhere between 3 and 4 because 5.43<412<5.44. The greatest integer of any value between 3 and 4 is 3, so the answer is 3. The greatest integer function is symbolized using the double bracket. See page 118 for a discussion of the greatest integer function.
5. Rewrite a logarithm using the change of base formula. Do not simplify or evaluate, just rewrite it. Look at problems 4.3.1-8.
6. Write the expression as a sum, difference, and/or constant multiple of logarithms and simplify (if possible). Three parts. Look at problems 4.3.23-42
7. Write the expression as the logarithm of a single quantity. Three parts. Look at problems 4.3.45-62
8. Solve the equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Four parts. Look at problems 4.4.43-56, 83-92.
9. Simplify the expressions. Thirteen parts. Look at problems 4.3.67-80 and 4.4.37-42
10. Identify the basic model of the graph. Nine graphs are shown, identify whether the model is constant, linear, quadratic, cubic, absolute value, square root, logarithmic, exponential, gaussian, logistic, polynomial, or rational. This is not matching, you need to know the names of the different models. Look at problems 4.5.1-6 and 4.6.1-8.
11. Identify the conic section or degenerate case. Choices are no graph, point, line, parallel lines, intersecting lines, parabola, circle, ellipse, and hyperbola. Nine parts.
12. 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. Two parts. Look at problems 7.3.9-24.
13. Find the equation of the parabola with vertex at the origin. Look at problems 7.1.11-18.
14. Find the equation of the ellipse with center at the origin. Look at problems 7.1.43-47.
15. Find the equation of the hyperbola with center at the origin. Look at problems 7.1.61-66.
16. Find the vertex, focus, and directrix of the parabola. Do not graph. Look at problems 7.2.17-24.
17. Find the center, foci, and vertices of the ellipse. Do not graph. Look at problems 7.2.33-36.
18. Find the center, foci, and vertices of the hyperbola. Also give the equations of the asymptotes. Do not graph. Look at problems 7.2.51-54.
19. Identify the conic section and write the equation based on the graph. If a parabola, give the focal length; if an ellipse, give the center; if a hyperbola, give the center. Look at problems 7.1.21-24, 39-42, and 67-68. Also look at problems 7.2.25-26, 41-42, and 61-62.
20. Same instructions as #19.
21. Same instructions as #19.
22. Complete the square to put a conic into standard form. Identify the type of conic, coordinates of the center (vertex for a parabola), and the change in x and change in y (for a hyperbola or ellipse) or focal length (for a parabola). Look at problems 7.2.37-40, 55-60.

## Notes

• No calculators allowed on the in-class portion 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 none of section 4.5 or 4.6 on the in-class test except for the matching.
• There is a take-home portion of the exam worth 25 points and is due the day of the exam.