49. Write a rational function with the following characteristics.

    1. Vertical asymptotes at x = 1 x equals 1  and x = − 3 , x equals negative 3 comma  horizontal asymptote at y = 1 , y equals 1 comma  zeros at 3 and 4
    2. Vertical asymptotes at x = 0 x equals 0  and x = 3 , x equals 3 comma  horizontal asymptote at y = 0 , y equals 0 comma  a zero at − 4 negative 4
    3. Vertical asymptotes at x = − 2 x equals negative 2  and x = 2 , x equals 2 comma  horizontal asymptote at y = 3 , y equals 3 comma  only one zero at − 1 . negative 1 .

Standardized Test Prep

SAT/ACT

GRIDDED RESPONSE

50. What is the x-coordinate of the hole in the graph of y = x 2 − 9 2 x 2 − x − 15 ? y equals . fraction x squared , minus 9 , over 2 , x squared , minus x minus 15 end fraction . question mark
51. Suppose z varies directly with x and inversely with y. If z is 1.5 when x is 9 and y is 4, what is z when x is 6 and y is 0.5?
52. What is the y-coordinate of the vertex of the parabola y = − 3 ( x − 4 ) 2 + 5 ? y equals negative 3 . open x minus 4 close squared . plus 5 question mark
53. What is the real solution of 54 x 3 − 16 = 0 54 x cubed , minus 16 equals 0  written as a fraction?
54. Using the Change of Base Formula, what is the value of log 7 15 log base 7 , 15  rounded to the nearest hundredth?

Mixed Review

See Lesson 8-2.

Sketch the asymptotes and the graph of each equation. Identify the domain and range.

55. y = 3 x + 4 y equals , 3 over x , plus 4
56. y = 2 x + 3 y equals . fraction 2 , over x plus 3 end fraction
57. y = − 1 x + 1 + 1 y equals . fraction negative 1 , over x plus 1 end fraction . plus 1
58. y = 5 x − 7 − 3 y equals . fraction 5 , over x minus 7 end fraction . minus 3
59. y = 4 x y equals , 4 over x
60. y = − 2 x − 1 + 2 y equals . fraction negative 2 , over x minus 1 end fraction . plus 2

See Lesson 6-7.

Find the inverse of each function. Determine if the inverse is a function.

61. y = 2 x − 3 y equals 2 x minus 3
62. y = 6 − x y equals 6 minus x
63. y = 2 x 2 y equals , 2 x squared
64. y = x 2 5 y equals , fraction x squared , over 5 end fraction
65. y = 1 x + 2 y equals . fraction 1 , over x plus 2 end fraction
66. y = x − 2 + 1 y equals , square root of x minus 2 end root , plus 1

See Lesson 1-5.

Solve each inequality. Graph the solution.

67. 6 a − 17 < 47 6 eh minus 17 less than 47
68. 2 ( x + 9 ) ≥ 90 2 open x plus 9 close greater than or equal to 90
69. 5 ( x − 11 ) + 13 ≥ 47 5 open x minus 11 close plus 13 greater than or equal to 47
70. 6 + y < 3 y − 2 6 plus y less than 3 y minus 2
71. 49 > 7 x + 28 49 greater than 7 x plus 28
72. 12 − 2 b > 3 ( b − 3 ) − 4 12 minus 2 b greater than 3 open b minus 3 close minus 4

Get Ready! To prepare for Lesson 8-4, do Exercises 73-76.

See Lesson 4-4.

Factor each expression.

73. 2 x 2 − 3 x + 1 2 x squared , minus 3 x plus 1
74. 4 x 2 − 9 4 x squared , minus 9
75. 5 x 2 + 6 x + 1 5 x squared , plus 6 x plus 1
76. 10 x 2 − 10 10 x squared , minus 10

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