Standardized Test Prep

SAT/ACT

63. What is the common ratio in the geometric sequence 4, 10, 25, 62.5, …?
    1. 0.4
    2. 2.5
    3. 15
    4. 25
64. The first term of a geometric sequence is 1 and its common ratio is 6. What is the sixth term?
    6. 31
    7. 3176
    8. 7776
    9. 46,656
65. Determine by inspection the end behavior of the graph of y = − 2 x 3 + 5 x − 4 . y equals negative , 2 x cubed , plus 5 x minus 4 .
    1. falls to the left, falls to the right: ( ↙ , ↘ ) open , south west arrow comma south east arrow , close
    2. falls to the left, rises to the right: ( ↙ , ↗ ) open , south west arrow comma north east arrow , close
    3. rises to the left, falls to the right: ( ↖ , ↘ ) open , north west arrow comma south east arrow , close
    4. rises to the left, rises to the right: ( ↖ , ↗ ) open , north west arrow comma north east arrow , close
66. What are the asymptotes of the graph of y = 10 x − 5 ? y equals . fraction 10 , over x minus 5 end fraction . question mark
    6. x = 0 , y = 5 x equals 0 comma y equals 5
    7. x = 5 , y = 0 x equals 5 comma y equals 0
    8. x = 5 , y = 10 x equals 5 comma y equals 10
    9. x = 10 , y = 5 x equals 10 comma y equals 5

Short Response

67. What are the points of discontinuity of y = x ( 2 x − 1 ) ( x + 1 ) ( x + 5 ) ( x + 1 ) ? y equals . fraction x . open , 2 x minus 1 , close . open , x plus 1 , close , over open , x plus 5 , close . open , x plus 1 , close end fraction . question mark

Mixed Review

See Lesson 9-2.

Write an explicit and a recursive formula for each arithmetic sequence.

68. − 3 , 0 , 3 , 6 , … negative 3 comma 0 comma 3 comma 6 comma dot dot dot
69. 17 , 8 , − 1 , … 17 comma 8 comma negative 1 comma dot dot dot
70. − 2 , − 13 , − 24 , … negative 2 comma negative 13 comma . negative 24 comma dot dot dot

See Lesson 6-2.

Simplify each expression. Rationalize all denominators. Assume that all variables are positive.

71. ( 7 ) ( 98 ) open square root of 7 close . open square root of 98 close
72. 3 6 7 2 x fraction 3 square root of 6 , over 7 , square root of 2 x end root end fraction
73. 6 x 4 y 6 x 2 y 3 fraction square root of 6 , x to the fourth , y end root , over square root of 6 , x squared , y cubed end root end fraction
74. ( 5 3 ) ( 150 3 ) open . cube root of 5 , , close open , cube root of 150 , . close

See Lesson 8-3.

Find the vertical asymptotes and holes for the graph of each rational function.

75. y = x − 3 x + 3 y equals . fraction x minus 3 , over x plus 3 end fraction
76. y = x − 3 x + 1 y equals . fraction x minus 3 , over x plus 1 end fraction
77. y = x − 3 x ( x − 1 ) y equals . fraction x minus 3 , over x . open , x minus 1 , close end fraction
78. y = x ( x + 3 ) ( x − 3 ) ( x + 3 ) y equals . fraction x . open , x plus 3 , close , over open , x minus 3 , close . open , x plus 3 , close end fraction

Get Ready! To prepare for Lesson 9-4, do Exercises 79–81.

See Problem 9-1.

Write a recursive formula for each sequence.

79. 1, 3, 6, 10, …
80. 1, 4, 9, 16, …
81. 1, 5, 14, 30, …

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