Objectives Assessed by MA 153 Test 3
Chapter 5 (not 5.4). 8.1, and Chapter 9 (not 9.5, 9.6)
(See also your quizzes, homework, and eHW assignments for more practice.)

1. Understand vertical and horizontal shifts of a function as an outside/inside additive change to the function rule.

Section 5.1 #2-25, 27-39, 41-45 and Chapter 5 Review #1-4, 17, 19, 26

2. Understand vertical or horizontal reflections of a function as an outside/inside change to the function rule by a negative sign.
Be able to combine these with shift transformations.
Section 5.2 #4-6, 8-19, 24, 25, 28, 29 and Chapter 5 Review #1-4, 27, 28

3. Identify whether a function is odd, even, or neither by looking at its graph, equation or table.

Section 5.2 #1-3, 20-23, 32, 34, 35, 42 and Chapter 5 Review 5-10 and Chapter 9 Review 37abcdefg and 39

4. If given that a function is odd or even and a point on its graph, determine another point.
Section 5.2 #30 and 31

5. Understand vertical stretch or compression of a function as an outside multiplicative change to the function rule.

Be able to combine these with reflections and shift transformations.
Section 5.3 #1-24, 28-38 and Chapter 5 Review #1-4, 18, 20, 23, 29, 37, 38

6. Understand the standard form, vertex form, and factored form of a parabola. Convert from standard form to vertex form by completing the square or using a grapher and a shift transformation. Section 5.5 #15, 16, 25-27

7. Find the vertex, axis of symmetry, concavity, whether the graph is narrower, wider, or same shape as y = x², and intercepts if given its equation. Be able to sketch without a graphing calculator.

Section 5.5 #1-6, 19-29, 34-35 and Chapter 5 Review #41

8. Find a quadratic model if given its zeros or its vertex and at least one other point.
Section 5.5 #7-14, 29 and Chapter 5 Review #13-16

9. Determine the composition f(g(x)). Simplify if necessary.

Section 8.1 #5, 7-10, 18-21 and Chapter 8 Review #1-11, 15h, 46

10. Know the six basic shapes of power functions (pages 378-379) and their equations. Know when they are flipped.

Section 9.1 #7-10, 25-31and Chapter 9 Review 7-8

11. Find the formula for a power function f(x) = kx^p if given that it passes through two points (a, f(a)) and (b, f(b)), where a = 1.

Section 9.1 #11-13, 19 and Chapter 9 Review 9

12. Find the formula for a power function f(x) = kx^p if given that it passes through two points (a, f(a)) and (b, f(b)), where a ≠ 1.

Section 9.1 #20-22 and Chapter 9 Review 10

13. Identify the degree, leading term, leading coefficient, and long-run behavior of a polynomial if given in expanded or factored form. Section 9.2 #1-10, 16, 18 and Chapter 9 Review 11-14

14. Determine the zeros of a polynomial if given its equation in expanded or factored form. If necessary, use a graphing calculator or try to factor.
Section 9.2 #12 and Section 9.3 #1-4, 8, 11-13, 37-42, 47 and Chapter 9 Review 15-16

15. Use a graphing calculator to find maximum or minimum values of a function as well as intersections.
Section 9.2 #13, 20, 23

16. Use the graph and the expanded form of a polynomial function to find its factored form.
Section 9.3 #5-7

17. Understand the (short-run) behavior of a polynomial function near its zeros. See Example 3 and the box on page 405.
Section 9.3 #9, 10, 14, 49

18. Find the formula for a polynomial from its graph.

Section 9.3 #15-20, 22-34, 48 and Chapter 9 Review 31-34, 36, 46, 47

19. Describe the long run behavior of a rational function. Report horizontal asymptotes, if they exist.

Section 9.4 #9-12, 16, 20 and Chapter 9 Review 44

Start your review by doing the following:

Check Your Understanding Chapter 5 (page 237): 1-21, 24-29

Check Your Understanding Chapter 8 (page 385): 2-7, 11-15

Check Your Understanding Chapter 9 (page 439): 1-43