C Challenge

Rewrite each function to make it easy to graph using transformations of its parent function. Describe the graph. Find the domain and range of each function.

55. y = − 2 ( 4 x − 3 ) y equals negative . square root of 2 . open , 4 x minus 3 , close end root
56. y = 3 x − 5 + 6 y equals . square root of 3 x minus 5 end root . plus 6
57. y = − 3 − 12 x + 18 y equals negative 3 minus . square root of 12 x plus 18 end root
58. 1. Graph y = − x , y equals , square root of negative x end root , comma   y = 1 − x , y equals , square root of 1 minus x end root , comma  and y = 2 − x . y equals , square root of 2 minus x end root , .
    2. Make a Conjecture How does the graph of y = h − x y equals , square root of h minus x end root  differ from the graph of y = x − h ? y equals , square root of x minus h end root , question mark
59. For what positive integers n are the domain and range of y = x n y equals , the th , root of x ,  the set of real numbers? Assume that x is a real number.

Standardized Test Prep

SAT/ACT

60. How is the graph of y = x − 5 y equals square root of x minus 5  translated from the graph of y = x ? y equals square root of x question mark
    1. shifted 5 units left
    2. shifted 5 units right
    3. shifted 5 units up
    4. shifted 5 units down

61. Which absolute value inequality has the graph shown here?

    

    6. | x − 1 | ≤ 3 vertical line x minus 1 vertical line less than or equal to 3
    7. | x − 1 | ≥ 3 vertical line x minus 1 vertical line greater than or equal to 3
    8. | x + 1 | ≤ 3 vertical line x plus 1 vertical line less than or equal to 3
    9. | x + 1 | ≥ 3 vertical line x plus 1 vertical line greater than or equal to 3
62. Which polynomial cannot be factored in the real number system?
    1. x 2 − 3 x + 2 x squared , minus 3 x plus 2
    2. x 2 + 4 x squared , plus 4
    3. 4 x 2 − 1 4 x squared , minus 1
    4. 2 x 2 y − 2 x y 2 2 , x squared , y minus . 2 x y squared

Short Response

63. How do the domains and ranges of the functions f ( x ) = x − 1 f , open x close , equals , square root of x minus 1 end root  and g ( x ) = x − 1 g , open x close , equals square root of x minus 1  compare?

Mixed Review

See Lesson 6-7.

Find the inverse of each function. Is the inverse a function?

64. f ( x ) = 2 3 x − 3 f , open x close , equals , 2 thirds , x minus 3
65. f ( x ) = x + 3 − 4 f , open x close , equals , square root of x plus 3 end root , minus 4
66. f ( x ) = ( 2 x + 1 ) 2 f open x close equals . open 2 x plus 1 close squared

See Lesson 6-2.

Rationalize the denominator of each expression. Assume that all variables are positive.

67. 36 x 3 12 y fraction square root of 36 , x cubed end root , over square root of 12 y end root end fraction
68. 3 x 2 y square root of fraction 3 x , over 2 y end fraction end root
69. x 3 3 y 3 fraction cube root of x , , over cube root of 3 y end root , end fraction
70. 3 x 3 2 y 5 the fifth , root of fraction 3 , x cubed , over 2 y end fraction end root ,

See Lesson 4-7.

Solve using the Quadratic Formula.

71. x 2 − 9 x + 15 = 0 x squared , minus 9 x plus 15 equals 0
72. 3 x 2 + 9 x = 27 3 x squared , plus 9 x equals 27
73. 5 x 2 + x = 3 5 x squared , plus x equals 3

Get Ready! To prepare for Lesson 7-1, do Exercises 74-76.

See Lesson 1-3.

Evaluate each expression for the given value of x .

74. 2 x 2 to the x  for x = 3 x equals 3
75. 4 x + 1 4 super x plus 1 end super  for x = 1 x equals 1
76. 2 3 x + 4 2 super 3 x plus 4 end super  for x = − 1 x equals negative 1

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