C Challenge

41. Writing Explain why 0 cannot be in the domain of an inverse variation.
42. Reasoning Suppose that ( x 1 , y 1 )  and  ( x 2 , y 2 ) open , x sub 1 , comma , y sub 1 , close , and , open , x sub 2 , comma , y sub 2 , close  are values from an inverse variation. Show that x 1 x 2 = y 2 y 1 . fraction x sub 1 , over x sub 2 end fraction . equals . fraction y sub 2 , over y sub 1 end fraction . .
43. Open-Ended The height h of a cylinder varies directly with its volume V and inversely with the square of its radius r. Find at least four ways to change the volume and radius of a cylinder so that its height is quadrupled.

Standardized Test Prep

SAT/ACT

44. Which equation represents inverse variation between x and y?
    1. x = y z x equals , y over z
    2. x = − 15 z y x equals negative , fraction 15 z , over y end fraction
    3. z = − 15 y x z equals negative , fraction 15 y , over x end fraction
    4. x z = 5 y x z equals , 5 to the y
45. How can you rewrite the expression ( 8 − 5 i ) 2 open 8 minus , 5 to the i , close squared  in the form a + bi?
    6. 39 + 80 i 39 plus , 80 to the i
    7. 39 − 80 i 39 minus , 80 to the i
    8. 89 + 80 i 89 plus , 80 to the i
    9. 89 − 80 i 89 minus , 80 to the i
46. The height of a ball thrown straight up from the ground with a velocity of 96 ft/s is given by the quadratic function h ( t ) = − 16 t 2 + 96 t . h open t close equals negative 16 , t squared , plus , 96 to the t , .  What is the maximum height the ball reaches?
    1. 6 ft
    2. 128 ft
    3. 144 ft
    4. 160 ft

47. Which expression is NOT equivalent to 81 x 4 y 8 6 the sixth , root of 81 , x to the fourth , y to the eighth end root ,

    6. ( 3 x y 2 ) 2 3 open . 3 x , y squared . close super 2 thirds end super
    7. ( 3 x ) 2 3 y 4 3 open , 3 x , close super 2 thirds end super . y super 4 thirds end super
    8. ( 3 x 2 y 2 ) 1 3 open . 3 , x squared , y squared . close super 1 third end super
    9. 9 x 2 y 4 3 cube root of 9 , x squared , y to the fourth end root ,

Short Response

48. What is the inverse of y = 4 x 2 + 5 ? y equals 4 , x squared , plus 5 question mark  Is the inverse a function?

Mixed Review

See Lesson 7-6.

Solve each equation. Check your answers.

49. l n 4 +  ln  x = 5 l n 4 plus , ln , x equals 5
50. l n x −  ln  3 = 4 l n x minus , ln , 3 equals 4
51. 2ln x + 3ln 4 = 4

See Lesson 6-2.

Multiply and simplify.

52. − 5 6 x ⋅ 3 6 x 3 negative 5 , square root of 6 x end root , dot 3 , square root of 6 , x cubed end root
53. 3 2 x 2 3 ⋅ 7 32 x 4 3 3 . cube root of 2 , x squared end root , . dot 7 . cube root of 32 , x to the fourth end root ,
54. 5 x 3 ⋅ 40 x y 7 square root of 5 , x cubed end root , dot . square root of 40 x , y to the seventh end root

See Lesson 6-1.

Simplify each radical expression. Use absolute value bars where they are needed.

55. x 10 y 100 square root of x to the tenth . y to the 100th end root
56. − 64 a 3 b 6 3 cube root of negative 64 , eh cubed , b to the sixth end root ,
57. 64 m 8 n 4 4 the fourth , root of 64 , m to the eighth , n to the fourth end root ,
58. x n n the th , root of x to the n end root ,

Get Ready! To prepare for Lesson 8-2, do Exercises 59-64.

See Lesson 2-7.

Graph each equation. Then describe the transformation of the parent function f(x) = | x |.

59. y = | x | + 2 y equals vertical line x vertical line plus 2
60. y = | x + 2 | y equals vertical line x plus 2 vertical line
61. y = | x | − 3 y equals vertical line x vertical line negative 3
62. y = | x − 3 | y equals vertical line x minus 3 vertical line
63. y = | x + 4 | − 5 y equals vertical line x plus 4 vertical line negative 5
64. y = | x − 10 | + 7 y equals vertical line x minus 10 vertical line plus 7

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