Extra Practice Skills Practice

Extra Practice Chapter 4

Skills Practice

Lesson

Tell whether the function shows growth or decay. Then graph.

4-1

4 2. f (x) = 20 _ 5 Explain whether each function is exponential. 4. f (x) = 4x 9 5. f (x) = 0.6 x

Lesson

4-2

()

1. f (x) = 12(2.4)

x

x

x

3. f (x) = 0.25(5) 6. f (x) = 10(0)

x

Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation. 7.

x

1

2

3

4

y

-1

0

2

4

8.

x

-3

-1

2

4

y

-3

-1

-1

-3

Use inverse operations to write the inverse of each function. x 9. f (x) = 15x 10. f (x) = x + 9 11. f (x) = _ 7 2x + 1 3x 12. f (x) = 3x + 2 13. f (x) = 5 - _ 14. f (x) = _ 4 5 Graph each function. Then write and graph its inverse. 15. f (x) = 2x + 4 16. f (x) = 0.8x + 1

Lesson

4-3

4x - 5 17. f (x) = _ 3

Write each exponential equation in logarithmic form. 18. 3 5 = 243 19. 51 0 = 1 20. 16 1.5 = 64

21. 7 x = 343

Write each logarithmic equation in exponential form. 22. log 64512 = 1.5 23. log 20.125 = -3 24. log 4x = 70

25. log x12 = 3

Evaluate by using mental math. 26. log 101000 27. log 50.2

29. log 1.11.21

28. log 0.50.125

Use the given x-values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function. 30. f (x) = 4 x; x = -2, -1, 0, 1, 2 31. f (x) = 0.2 x; x = -2, -1, 0, 1, 2

Lesson

4-4

Express as a single logarithm. Simplify, if possible. 33. log 48 + log 42 32. log 210 + log 212.8

34. log 51.25 + log 54

35. log 6144 - log 64

36. log10,000 - log100

37. log 88 - log 81

Simplify, if possible. 38. log 864 4

39. log 749 5

40. log 91 4

41. log 33 5x+8

42. 4 log 412

43. log 1.41.4 5

Evaluate. 44. log 4256

( )

1 45. log 4 _ 64

46. log 37

EPS8

47. log 413

Extra Practice Chapter 4 Lesson

4-5

Lesson

4-6

Lesson

4-7

Solve and check. 48. 3 x+1 = 9 4

Skills Practice

49. 32 x-2 = 8 x

50. 9 x = 12

Solve. 52. log 6(4x - 9) = log 6(x)

53. log 7(10x + 13) = 3

55. log 9x 3 = 8

56. log x + log(2x - 1) = 1

51. 3.5 2x-1 = 15 54. log(20x) - log4 = 2 2 +2=0 57. log 3 _ x

()

Use a table and a graph to solve. 58. 3 4x-x = 243 59. 3 x4 x ≥ 1728

60. log x 3 = x - 94

61. 3log x 2 < 6

Graph. 62. f (x) = e x - 1

63. f (x) = -2e x + 3

64. f (x) = 2 - e -x

65. f (x) = 1.5e x+1

Simplify. 66. ln e 20

67. ln e 2x+10

68. e ln 5x

2

69. e 2 ln 2x

Make a table of values and graph each function. Describe the asymptote, the domain, and the range. Tell how the graph is transformed from the graph of f (x) = 4 x. 70. g (x) = 4 x - 2 71. h (x) = 4 x+2 72. j (x) = 4 x-1 - 4 Graph each exponential function. Find the y-intercept, the asymptote, the domain, and the range. Describe how the graph is transformed from the graph of its parent function. 1 (3 x) 73. g (x) = -_ 2

74. h (x) = 3(2 -x)

75. j (x) = 5e x+1

Graph each logarithmic function. Find the asymptote. Then describe how the graph is transformed from the graph of its parent function. 76. g (x) = -4 log x 77. h (x) = 3 ln(3 - x) 78. j (x) = ln(0.5x) - 3 Write each transformed function by using the given parent function and the indicated transformations. 79. The parent function f (x) = 6 x is horizontally stretched by a factor of 3 and translated 4 units to the left. 1 , reflected 80. The parent function f (x) = log x is vertically compressed by a factor of _ 5 across the y-axis, and translated 10 units down.

Lesson

4-8

Determine whether f is an exponential function of x. If so, find the constant ratio. 81. 82. x -2 -1 1 2 3 x -2 -1 0 1 2

83.

y

0.4

2

10

50

250

x

-2

-1

0

1

2

y

4

2

1

0.5

0.25

84.

EPS9

y

-17

-2

13

28

43

x

-2

-1

0

1

2

y

-6

1

12

37

54