Math 121 - Exam 1 Study Guide

1. Use the table of values to evaluate the combination and composition of functions. Eight parts. Look at problem 1.4.53 and supplemental exercise 1.15.
2. Rewrite the function without absolute value notation. Look at problem 1.2.13-14.
3. Identify each function as odd, even, or neither. Two parts. Look at problem 1.4.69
4. Determine whether the graph of each relation is symmetric about the x-axis, y-axis, or origin. Four parts. Look at problems 1.4.70-71.
5. Given the value of one trigonometric function, draw an appropriate triangle and find the values of the other five trigonometric functions. Look at problems 15-16 in Appendix E.
6. Identify the translation and the new domain and range for each function. Eight parts. Similar to the example worked in class or look at the lecture notes for section 1.5 from College Algebra.
7. Complete the identities for the addition, subtraction, double angle, or half angle formulas from trig. Four parts. Look at formulas 34-46 in Appendix E.
8. Simplify trigonometric functions. Ten parts. Look at problem 1.6.33
9. Find the dimensions of a solid that minimize the surface area. Look at problem 1.1.11. The geometric formulas necessary are given on the test.
10. Consider a polynomial function. Know the number of real or complex zeros, the maximum number of turns, the right hand behavior, and the left hand behavior of the graph. Look at the review of polynomials on page 68 and the section 3.2 lecture notes from College Algebra.
11. Consider a rational function. Know whether the graph will touch or cross the x-axis, the right hand behavior (horizontal asymptotes), behavior at vertical asymptotes, and left hand behavior. Read the review of rational functions on page 69 and the section 3.5 lecture notes from College Algebra.
12. Consider the position curve shown in the graph. Describe the motion of the particle in words and find the average velocity over a given interval. Look at problems 1.5.27-31.
13. Match the graph with the function. Eight parts. Look at problem 1.6.11.

Notes:

• Problems are similar to those in the textbook.