1. Slide 2 - 1 MAT 171 Chapter 2 Review The following is a brief review of Chapter 2 for Test 2 that covers Chapters 2 & 3 and Section 10.7. This does NOT cover all the material that may be on the test. Click on Slide Show and View Slide Show. Read and note your answer to the question. Advance the slide to see the answer. Dr. Claude Moore, Math Instructor, CFCC

2. Slide 2 - 2 Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. Chapter 2

3. Slide 2 - 3 Copyright © 2009 Pearson Education, Inc. Chapter 2: More on Functions 2.1Increasing, Decreasing, and Piecewise Functions; Applications 2.2The Algebra of Functions 2.3The Composition of Functions 2.4Symmetry and Transformations 2.5Variation and Applications

4. Slide 2 - 4 Copyright © 2009 Pearson Education, Inc. a. (0, 1) c. (  3, 0) b. (  4,  3) d. (1, 2) Determine the interval on which the function is increasing.

5. Slide 2 - 5 Copyright © 2009 Pearson Education, Inc. a. (0, 1) c. (  3, 0) b. (  4,  3) d. (1, 2) Determine the interval on which the function is increasing.

6. Slide 2 - 6 Copyright © 2009 Pearson Education, Inc. a. rel max 0 at x = 0; rel min 4 at x = –32 c. rel max 32 at x = 4; rel min 0 at x = 0 b. rel max 0 at x = 0; rel min –32 at x = 4 d. There are no relative extrema. Use a graphing calculator to find any relative maxima or minima of

7. Slide 2 - 7 Copyright © 2009 Pearson Education, Inc. a. rel max 0 at x = 0; rel min 4 at x = –32 c. rel max 32 at x = 4; rel min 0 at x = 0 b. rel max 0 at x = 0; rel min –32 at x = 4 d. There are no relative extrema. Use a graphing calculator to find any relative maxima or minima of

8. Slide 2 - 8 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Trisha and Gordon drive away from a campground at right angles to each other. Trisha’s speed is 70 mph and Gordon’s speed is 55 mph. Express the distance between the cars as a function of time.

9. Slide 2 - 9 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Trisha and Gordon drive away from a campground at right angles to each other. Trisha’s speed is 70 mph and Gordon’s speed is 55 mph. Express the distance between the cars as a function of time.

10. Slide 2 - 10 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which piecewise function matches the graph?

11. Slide 2 - 11 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which piecewise function matches the graph?

12. Slide 2 - 12 Copyright © 2009 Pearson Education, Inc. a. 2 c. 7 b. 0 d. 5 Find f (–1) if

13. Slide 2 - 13 Copyright © 2009 Pearson Education, Inc. a. 2 c. 7 b. 0 d. 5 Find f (–1) if

14. Slide 2 - 14 Copyright © 2009 Pearson Education, Inc. a. 5 c. 1 b. d. 4 Find f (2) if

15. Slide 2 - 15 Copyright © 2009 Pearson Education, Inc. a. 5 c. 1 b. d. 4 Find f (2) if

16. Slide 2 - 16 Copyright © 2009 Pearson Education, Inc. a. x + 5 c. x 2 + 5 b. x 2 – x – 1 d. x 2 + x + 5 Given that f (x) = x + 3 and g (x) = x 2 + 2, find ( f + g) x.

17. Slide 2 - 17 Copyright © 2009 Pearson Education, Inc. a. x + 5 c. x 2 + 5 b. x 2 – x – 1 d. x 2 + x + 5 Given that f (x) = x + 3 and g (x) = x 2 + 2, find ( f + g) x.

18. Slide 2 - 18 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Given that f (x) = x 2 – 4 and, find the domain of g/f.

19. Slide 2 - 19 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Given that f (x) = x 2 – 4 and, find the domain of g/f.

20. Slide 2 - 20 Copyright © 2009 Pearson Education, Inc. a. 3 c. –7h b. –7 d. 3 – 7x – 7h Construct and simplify the difference quotient for f (x) = –7x + 3.

21. Slide 2 - 21 Copyright © 2009 Pearson Education, Inc. a. 3 c. –7h b. –7 d. 3 – 7x – 7h Construct and simplify the difference quotient for f (x) = –7x + 3.

22. Slide 2 - 22 Copyright © 2009 Pearson Education, Inc. a. 2x + 6 c. 2xh + h 2 + 6h b. x 2 + 2xh + 6x + h 2 + 6h d. 2x + h + 6 Construct and simplify the difference quotient for f (x) = x 2 + 6x.

23. Slide 2 - 23 Copyright © 2009 Pearson Education, Inc. a. 2x + 6 c. 2xh + h 2 + 6h b. x 2 + 2xh + 6x + h 2 + 6h d. 2x + h + 6 Construct and simplify the difference quotient for f (x) = x 2 + 6x.

24. Slide 2 - 24 Copyright © 2009 Pearson Education, Inc. a. h(x) = 2x 2 + 4 c. h(x) = 2x 2 + 16x + 32 b. h(x) = 2x 3 + 8x 2 d. h(x) = 2x 2 + x + 4 For f(x) = x + 4 and g(x) = 2x 2, find

25. Slide 2 - 25 Copyright © 2009 Pearson Education, Inc. a. h(x) = 2x 2 + 4 c. h(x) = 2x 2 + 16x + 32 b. h(x) = 2x 3 + 8x 2 d. h(x) = 2x 2 + x + 4 For f(x) = x + 4 and g(x) = 2x 2, find

26. Slide 2 - 26 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Forand g(x) = x 2, find the domain of

27. Slide 2 - 27 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Forand g(x) = x 2, find the domain of

28. Slide 2 - 28 Copyright © 2009 Pearson Education, Inc. a. c. b. d. For f(x) = 3x – 4 and g(x) =, find h(x) = (fg)(x).

29. Slide 2 - 29 Copyright © 2009 Pearson Education, Inc. a. c. b. d. For f(x) = 3x – 4 and g(x) =, find h(x) = (fg)(x).

30. Slide 2 - 30 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following is symmetric with respect to the origin?

31. Slide 2 - 31 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following is symmetric with respect to the origin?

32. Slide 2 - 32 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following functions is even?

33. Slide 2 - 33 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following functions is even?

34. Slide 2 - 34 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Write an equation for a function that has the shape of but is shifted left 3 units and down 5 units.

35. Slide 2 - 35 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Write an equation for a function that has the shape of but is shifted left 3 units and down 5 units.

36. Slide 2 - 36 Copyright © 2009 Pearson Education, Inc. a. c. b. d. If (  3, 6) is a point on the graph of y = f (x), what point do you know is on the graph of y = f (x + 3)?

37. Slide 2 - 37 Copyright © 2009 Pearson Education, Inc. a. c. b. d. If (  3, 6) is a point on the graph of y = f (x), what point do you know is on the graph of y = f (x + 3)?

38. Slide 2 - 38 Copyright © 2009 Pearson Education, Inc. a. c. b. d. The graph of y = f (x) is given. Which graph below represents the graph of y = f (x) – 1?

39. Slide 2 - 39 Copyright © 2009 Pearson Education, Inc. a. c. b. d. The graph of y = f (x) is given. Which graph below represents the graph of y = f (x) – 1?

40. Slide 2 - 40 Copyright © 2009 Pearson Education, Inc. a. c. b. d. The graph of f is given. Which graph below represents the graph of g(x) = 2f (x) + 1?

41. Slide 2 - 41 Copyright © 2009 Pearson Education, Inc. a. c. b. d. The graph of f is given. Which graph below represents the graph of g(x) = 2f (x) + 1?

42. Slide 2 - 42 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following is symmetric with respect to the y-axis?

43. Slide 2 - 43 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Which of the following is symmetric with respect to the y-axis?

44. Slide 2 - 44 Copyright © 2009 Pearson Education, Inc. a. 2 c.  2 b. 72 d. If y varies inversely as x and y = 12 when x = 30, find y when x = 5.

45. Slide 2 - 45 Copyright © 2009 Pearson Education, Inc. a. 2 c.  2 b. 72 d. If y varies inversely as x and y = 12 when x = 30, find y when x = 5.

46. Slide 2 - 46 Copyright © 2009 Pearson Education, Inc. a. 33.6 in 3 c. 32.0 in 3 b. 56.8 in 3 d. 72.3 in 3 The volume of a 6-in. tall cone varies directly as the square of the radius. The volume is 14.2 in 3 when the radius is 1.5 in. Find the volume when the radius is 3 in.

47. Slide 2 - 47 Copyright © 2009 Pearson Education, Inc. a. 33.6 in 3 c. 32.0 in 3 b. 56.8 in 3 d. 72.3 in 3 The volume of a 6-in. tall cone varies directly as the square of the radius. The volume is 14.2 in 3 when the radius is 1.5 in. Find the volume when the radius is 3 in.

48. Slide 2 - 48 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Find an equation of variation where y varies jointly as the square of x and the square of z and inversely as w, and y = 50 when x = 2, z = 3, and w = 10.

49. Slide 2 - 49 Copyright © 2009 Pearson Education, Inc. a. c. b. d. Find an equation of variation where y varies jointly as the square of x and the square of z and inversely as w, and y = 50 when x = 2, z = 3, and w = 10.

50. Slide 2 - 50 Copyright © 2009 Pearson Education, Inc. a. 0.5 c. 15.2 b. 12.5 d. 0.08 If y varies inversely as x and y = 0.2 when x = 10, find y when x = 25.

51. Slide 2 - 51 Copyright © 2009 Pearson Education, Inc. a. 0.5 c. 15.2 b. 12.5 d. 0.08 If y varies inversely as x and y = 0.2 when x = 10, find y when x = 25.

52. Slide 2 - 52 Copyright © 2009 Pearson Education, Inc. a. 0.25 ampere c. 0.16 ampere b. 1.25 ampere d. 0.08 ampere The current I in an electrical conductor varies inversely as the resistance R of the conductor. Suppose I is 0.2 amperes when the resistance is 200 ohms. Find the current when the resistance is 250 ohms.

53. Slide 2 - 53 Copyright © 2009 Pearson Education, Inc. a. 0.25 ampere c. 0.16 ampere b. 1.25 ampere d. 0.08 ampere The current I in an electrical conductor varies inversely as the resistance R of the conductor. Suppose I is 0.2 amperes when the resistance is 200 ohms. Find the current when the resistance is 250 ohms.