Standardized Test Prep

SAT/ACT

49. What is an equation for the translation of y = 2 x y equals , 2 over x  that has asymptotes at x = 3  and  y = − 5 ? x equals 3 , and , y equals negative 5 question mark
    1. y = 2 x − 3 − 5 y equals . fraction 2 , over x minus 3 end fraction . minus 5
    2. y = 2 x + 3 + 5 y equals . fraction 2 , over x plus 3 end fraction . plus 5
    3. y = 2 x + 5 − 3 y equals . fraction 2 , over x plus 5 end fraction . minus 3
    4. y = 2 x − 5 + 3 y equals . fraction 2 , over x minus 5 end fraction . plus 3
50. The graph below shows which inequality?

    

    6. y < − 2 . 5 x + 5 y less than , minus 2 . , 5 to the x , plus 5
    7. 2.5 x + y ≥ 5 2.5 x plus y greater than or equal to 5
    8. − 2.5 x + y < 5 negative 2.5 x plus y less than 5
    9. 5 x + y ≤ 5 5 x plus y less than or equal to 5
51. If p and q vary inversely, and p = 10 p equals 10  when q = − 4 , q equals negative 4 comma  what is q when p = − 2 ? p equals negative 2 question mark
    1. 20
    2. 4 5 4 fifths
    3. − 4 5 negative , 4 fifths
    4. − 20 negative 20
52. Which equation represents the inverse of the graph below?

    

    6. y = log 3 x y equals , log base 3 , x
    7. x = log 3 y x equals , log base 3 , y
    8. y = log x 3 y equals , log base x , 3
    9. x = log y 3 x equals , log base y , 3

Short Response

53. What is b if the graph of y = 27 b x y equals 27 , b to the x  includes the point ( − 1 , 81 ) ? open negative 1 comma 81 close question mark

Mixed Review

See Lesson 8-1.

Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x = − 5 . x equals negative 5 .

54. x = 2 x equals 2  when y = 12 y equals 12
55. x = 25 x equals 25  when y = 2 y equals 2
56. x = 12 x equals 12  when y = 4 y equals 4

See Lesson 7-1.

Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the y-intercept.

57. y = 3 ( 4 ) x y equals 3 . open 4 close to the x
58. y = 0.1 ( 2 ) x y equals 0.1 . open 2 close to the x
59. y = 5 ( 0.8 ) 8 y equals 5 . open 0.8 close to the eighth
60. y = 3 ( 1 2 ) x y equals 3 . open , 1 half , close to the x

See Lesson 6-3.

Multiply.

61. ( 5 3 − 2 ) 2 open 5 square root of 3 minus 2 close squared
62. ( 4 + 2 3 ) ( 6 − 3 3 ) open 4 plus 2 square root of 3 close open 6 minus 3 square root of 3 close
63. ( 3 + 5 ) ( 3 − 5 ) open square root of 3 plus square root of 5 close open square root of 3 minus square root of 5 close

Get Ready! To prepare for Lesson 8-3, do Exercises 64-67.

See Lesson 4-4.

Factor each expression.

64. x 2 − 6 x + 8 x squared , minus 6 x plus 8
65. x 2 + 6 x − 27 x squared , plus 6 x minus 27
66. 2 x 2 + x − 28 2 x squared , plus x minus 28
67. 2 x 2 − 19 x + 24 2 x squared , minus 19 x plus 24

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