Chapter 9 Radical Functions

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Homework 9.4 SSM: Intermediate Algebra 41. ( ) f 9c = 7 9c − 3 = 7 ⋅3 c − 3 = 21 c − 3 43. h( x) = ( x + 3) + ( x − 5) = x + 3 + x − 5 = 2 x − 2 45. h( x) = ( x − 5) − ( x − 3) 47. h( x) = x − x − 5 − 3 = −8 = ( x + 3) ( x − 5) x + 3 x + 5 = ⋅ x − 5 x + 5 = x ⋅ x + x ⋅ 5 + 3⋅ x + 3⋅5 ( x ) − ( 5) 2 2 x + 5 x + 3 x + 15 = x − 25 x + 8 x + 15 = x − 25 49. h( x) = ( 5 x − 9) + ( 4 x + 1) = 5 x − 9 + 4 x + 1 = 9 x − 8 51. h( x) = ( 4 x + 1) − ( 5 x − 9) = 4 x + 1− 5 x + 9 = − x + 10 53. h( x) 5 x − 9 = 4 x + 1 5 x − 9 4 x −1 = ⋅ 4 x + 1 4 x −1 5 x ⋅ 4 x − 5 x ⋅1− 9⋅ 4 x + 9⋅1 = ( 4 x ) − ( 1) 2 2 20x − 5 x − 36 x + 9 = 16x −1 20x − 41 x + 9 = 16x −1 55. h( x) = ( 2 x − 3 5) + ( 2 x + 3 5) = 2 x − 3 5 + 2 x + 3 5 = 4 x 57. h( x) = ( 2 x + 3 5) −( 2 x − 3 5) 59. h( x) = 2 x + 3 5 − 2 x + 3 5 = 6 5 2 x − 3 5 = 2 x + 3 5 2 x − 3 5 2 x − 3 5 = ⋅ 2 x + 3 5 2 x − 3 5 = ( 2 x ) − 2( 2 x )( 3 5) + ( 3 5) 2 2 ( 2 x ) − ( 3 5) 2 2 4x − 12 5x + 45 = 4x − 45 61. h( x) = ( x + 1 − 2) + ( x + 1 + 2) = x + 1 − 2 + x + 1 + 2 = 2 x + 1 63. h( x) = ( x + 1 + 2) − ( x + 1 − 2) = x + 1 + 2 − x + 1 + 2 = 4 288
SSM: Intermediate Algebra Homework 9.5 65. h( x) = x + 1 − 2 x + 1 + 2 x + 1 − 2 x + 1 − 2 = ⋅ x + 1 + 2 x + 1 − 2 = ( x + 1) − 2( x + 1)( 2) + ( 2) 2 2 ( x + 1) − ( 2) x + 1− 4 x + 1 + 4 = x + 1− 4 x − 4 x + 1 + 5 = x − 3 2 2 67. a. The square root model would fit best because it continues to increase slowly. The quadratic function would reach a peak and then start to decrease. 79. Answers may vary. The graph of f can be found by translating the graph of y = a x horizontally by h units (left if h < 0 and right if h > 0 ), and vertically by k units (up if k > 0 and down if k < 0 ). Homework 9.5 1. x = 5 ( ) 2 2 x = 5 x = 25 Check x = 25 ( ) = ? 25 5 5 = 5 true The solution is 25. b. S ( 20) = 3.9 20 + 280 ≈ 297.44 The average test score in 2002 would be about 297. c. S ( 23) = 3.9 23 + 280 ≈ 298.70 The average test score in 2005 would be about 299. 69. f ( − 6) = 0 71. f ( 0) = 2.4 73. x = − 6 75. x = 3 77. ( ) ( ) f x = 2 x + 3 + 2; g x = − 2 x + 3+ 2 The graph looks like a parabola that opens to the right. The relation is not a function because it would fail the vertical line test. 3. 5. 7. x = −2 ( x ) = ( −2) 2 2 x = 4 Check x = 4 ( ) ? 4 =− 2 ? 2 =− 2 false There are no real solutions. 3 x − 1 = 5 3 x = 6 x = 2 ( ) 2 2 x = 2 x = 4 Check x = 4 ( ) ? 3 4 − 1= 5 5 = 5 true The solution is 4. 4 − 5 x = 2 x −10 − 7 x = −14 x = 2 ( ) 2 2 x = 2 x = 4 Check x = 4 289
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Chapter 9 Radical Functions

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