A1© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice

Answers to Algebra 2 Unit 4 PracticeLeSSon 19-1 1. D

2. a. 24, 26, 28, 210, 212

b. 22, 0, 2, 4, 6

c. 23, 0, 3, 6, 9

3. a. 5

b. 4

c. 22

4. There is no common difference.

5. She is incorrect. The sequence is arithmetic with a common difference of 4. The next two terms are 23 and 27.

LeSSon 19-2 6. C

7. a. 299

b. 1057

c. 690

8. a. 2505

b. 5445

c. 8030

9. 50.05

10. a. 61

b. 257

c. 168

LeSSon 19-3 11. B

12. B

13. 222.5

14. 19

15. 211

LeSSon 20-1 16. neither

17. geometric, r 5 3

18. 49,152

19. False, the common ratio is 6: 14

(6) 5 64

, 64

(6) 5 9.

20. 4.71 meters

LeSSon 20-2 21. C

22. D

23. a. 2425

b. 243,688

c. 11.56

d. 2180

24. a. an 5 5n 1 1

b. 19,530

25. 8

LeSSon 20-3 26. C

27. a. 28

b. does not exist: r $ 1

c. does not exist: r $ 1

d. 100,000

28. a. diverges

b. converges

c. diverges

d. diverges

29. r 5 14

30. Tuscany’s mom is correct: 20 12n

n

0∑

=

∞

5 40.

A2© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice

LeSSon 21-1 31. The graph will be a straight line.

32. a. x 1 2 3 4 5

f (x) 2.7 4.5 6.3 8.1 9.9

b. f (x) 5 1.8x 1 0.9

33. A

34. a. yes

b. yes

c. yes

35. C

LeSSon 21-2 36. C

37. A

38. a. exponential, f (x) 5 4814

x

b. linear, f (x) 5 6x 1 2

c. neither ( f (x) 5 x2)

39. a. 66%

b. 0.66

c. x 5 {1, 2, 3, 4, 5, 6, 7, 8, 9}, f (x) 5 {30, 10, 3.33, 1.11, 0.37, 0.12, 0.03, 0.01, 0.005}; the domain is positive since they represent the number of purchases; Tony spends his last whole cent on the ninth purchase. (Some students may choose to include 0 in the domain and 90 in the range.)

40. f (x) 5 7.5 13

x

; decay function.

LeSSon 21-3 41. The graphs are the same because the functions

are equal: f(x) 5 13

x

5

13

x

x 5 13x 5 32x.

42. exponential function

43. D

44. a. (2∞, ∞); (0, ∞); increases; (0, 3)

b. (2∞, ∞); (0, ∞); decreases; (0, 5)

c. (2∞, ∞); (2∞, 0); increases; (0, 22)

d. (2∞, ∞); (2∞, 0); increases; (0, 21)

45. The function is decreasing for all a , 0.

LeSSon 21-4 46. reflection over the x-axis

47. a.

x

y

g(x) f(x)

25210

5

10

15

5 10

b. y 5 2

c. vertical stretch by factor of 2, reflection over the y-axis, vertical shift by 12

48. horizontal shift to the left by 4

49. vertical shift up by 4

50. for all a , 0

LeSSon 21-5 51. C

52. B

53. a 5 2 and a 5 3

54. a.

x

y

210 25

210

25

10

5

5 10

g(x)

f(x)

A3© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice

b. vertical stretch by factor of 3, vertical shift down by 2

c. domain (2∞, ∞), range (22, ∞), asymptote at y 5 22

55. g(x) 5 22.8(ex 2 4.2)

LeSSon 22-1 56. A magnitude 8.0 earthquake indicates 1000 times

the ground motion of a magnitude 5.0 earthquake.

57. Yes; an earthquake with a magnitude of 4.0 and lower will rarely cause damage. An earthquake with magnitude of 6.0 may cause some damage, but a magnitude of 8.0 is devastating.

58. No; a magnitude 0.0 earthquake indicates ground motion of 0.001 cm.

59. a. 631 times

b. 3981 times

c. 50,119 times

d. 12,589,254 times

60. between 4 and 5

LeSSon 22-2 61. a. magnitude 3.3

b. magnitude 4.4

c. magnitude 7.7

d. magnitude 9.8

62. a. log 1000 5 3

b. log 1,000,000 5 6

c. log 1100

5 22

d. log 1

10,000 5 24

63. a. 104 5 10,000

b. 102 5 100

c. 1024 5 1

10,000

d. 1027 5 1

10,000,000 64. a. n

b. b

65. D

LeSSon 22-3 66. a. log 5 1 log x

b. log 3 2 log y

c. 4 log x

d. 3 log m 2 log 4

67. a. 20.195

b. 0.195

c. 1.885

68. a. log yx

47

b. log xy

5

2

c. log xy44 3

d. log ab

69. C

70. log (5)(13) 5 log 5 1 log 13 5 1.8

LeSSon 22-4 71. No; by the Power and Product Properties,

log xy2 5 log x 2 2 log y.

72. Yes; log 10 5 log (5)(2) 5 log 5 1 log 2 and log mn 5 log (m)(n) 5 log m 1 log n.

73. The Quotient Property states that

log uy

2

5 5 log u2 2 log y5, and the Power Property

states that log u2 2 log y5 5 2 log u 2 5 log y.

74. a. log 10,000 5 4

b. log 1 5 0

c. log 10 5 1

75. C

LeSSon 23-1 76. D

77. a. x

b. x

c. y

A4© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice

78. x 5 3y 2 4,

x 1 4 5 3y,

y 5 x 431

,

f 21(x) 5 x 431

79. The line of symmetry between a function and its inverse is y 5 x.

80. a. g (x) 5 log14

(x)

b. g (x) 5 x 251

c. g (x) 5 x7

22

d. g (x) 5 log5 x

e. g (x) 5 ex

LeSSon 23-2 81. a. log5 125 5 3

b. log7 1343

5 23

c. log 1 5 0

d. log4 64 5 3

82. a. 34 5 81

b. 93 5 729

c. e0 5 1

d. 623 5 1216

83. 4

84. log1024 1 5 0; any number to the power of 0 is 1.

85. A

LeSSon 23-3 86.

x 22 21 0 1 2

f ( x) 5 3x19

13

1 3 9

87. x

19

13 1 3 9

g A4 (x) 5 log3 x 22 21 0 1 2

88.

x

y

210 25

210

25

10

5

5 10

(0, 1)

f (x)

g(x)

(1, 0)

89. f(x) 5 3x : domain (2∞, ∞), range (0, ∞)

g(x) 5 log3 x: domain (0, ∞), range (2∞, ∞)

90. B

LeSSon 24-1 91. C

92. a. x 5 2

b. x 5 2

c. x 5 43

d. x 5 23

93. a. x 5 158

b. x 5 2

c. x 5 34

d. x 5 32

94. 15

ln 3

95. 13

ln 26

LeSSon 24-2 96. D

97. A

A5© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice

98. a. x ≈ 4

b. x ≈ 3

c. x ≈ 2

d. x ≈ 3

99. a. x 5 3.907

b. x 5 3.170

c. x 5 2.154

d. x = 2.912

100. x 5 1.105

LeSSon 24-3 101. A

102. B

103. a. x 5 6

b. x 5 223

c. x 5 27

d. x 5 26

104. a. x 5 9

b. x 5 227

c. x 5 113

d. no solution

105. a. (4, ∞)

b. (25, ∞)

c. (4.5, ∞)

d. (223

, ∞)

LeSSon 24-4 106. B

107. a. x $ 397.164

b. 1.667 , x # 14.937

c. x $ 0.546

108.

x

y

23 22 21

23

22

21

2

3

4

1

5

1 2 3 4 5

(3.75, 3.42)

0 # x # 3.75

109. x . 1.410

110. 2.333 , x # 3.861