# Math 116 - Chapter 4 Study Guide

No Calculators are allowed on this exam.

1. Look at the graph of a relation. Determine if the graph is that of a function, a one-to-one function, or neither.
2. Find the inverse of the function. Look at problems 1.7.41-51
3. Solve the exponential equation for x. Two parts. Look at problems 4.4.17-24
4. Solve the logarithmic equation for x. Two parts. Look at problems 4.4.29-34
5. Rewrite the exponential expression in logarithmic form. Look at problems 4.2.9-16
6. Rewrite the logarithmic expression in exponential form. Look at problems 4.2.1-8
7. 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.
8. Rewrite a logarithm using the change of base formula. Do not simplify or evaluate, just rewrite it. Look at problems 4.3.1-8.
9. Given the value of the logarithm of some numbers, evaluate the logarithm of a product, quotient, or power. Three parts. Look at problems 4.3.102 and problem 2 on the take home exam.
10. For each exponential function, describe how the graph shown differs from the basic exponential graph (give its transformation) and then write an equation for the graphed function. Five parts. Look at problems. Look at problems 4.1.15-22.
11. 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
12. Write the expression as the logarithm of a single quantity. Three parts. Look at problems 4.3.45-62
13. For each logarithmic function, describe how the graph shown differs from the basic logarithmic graph (give its transformation) and then write an equation for the graphed function. Five parts. Look at problems. Look at problems 4.2.45-52.
14. Simplify the expressions without the use of a calculator. Twelve parts. Look at problems 4.3.67-80 and 4.4.37-42
15. Identify the basic model of the graph. Eight 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.
16. Solve the exponential equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Two parts. Look at problems 4.4.43-56. Especially pay attention to 55 and 56.
17. Solve the logarithmic equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Three parts. Look at problems 4.4.83-92

## 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 class period after the in-class portion.
• Even though the take home is not due until after the regular exam, you may want to work on it before the exam because some of the problems on the take home may help you with the in-class exam.

## Point values for each question

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total 3 3 3 3 2 2 3 2 4 5 6 6 5 12 4 6 6 75