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. 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.
5. 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.
6. Consider a rational function. Know whether the graph will touch or cross the x-axis, the right hand and left hand behavior (horizontal asymptotes), behavior at vertical asymptotes. Read the review of rational functions on page 69 and the section 3.5 lecture notes from College Algebra.
7. 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.
8. 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.
9. Use trigonometric identities to simplify the expression. Two parts.
10. Find the exact value using the sum or difference of two angles formula for sine, cosine, or tangent.
11. Identify the translation and the new domain and range for each function. Six parts. Similar to the example worked in class or look at the lecture notes for section 1.5 from College Algebra.
12. A function is given. Find the slope of the secant line between the two given points on the curve.
13. Simplify trigonometric functions. Eight parts. Look at problem 1.6.33
14. Consider the position curve shown in the graph. Find the instantaneous velocity at a point and the average velocity over a given interval. Look at problems 1.5.27-31.
15. A situation involving rectilinear motion is described. Sketch a position vs time curve that could represent that motion.

Notes:

• Most problems are similar to those in the textbook.