Section 4.7 AN29 45. Step 1: ( ) = + f x x x 1 2 ; domain: { } ≠ x x 0 Step 2: f is in lowest terms Step 3: no y-intercept; no x-intercepts Step 4: f is in lowest terms; vertical asymptote: = x 0 Step 5: Oblique asymptote: = y x, not intersected Step 6: 5 25 25 5 Step 7: y 5 x 5 (21, 22) (1, 2) x 5 0 y 5 x 47. Step 1: ( ) ( ) ( ) = + = + − + f x x x x x x x 1 1 1 3 2 ; domain: { } ≠ x x 0 Step 2: f is in lowest terms Step 3: no y-intercept; x-intercept:−1 Step 4: f is in lowest terms; vertical asymptote: = x 0 Step 5: No horizontal or oblique asymptote Step 6: 10 25 210 5 Step 7: y 5 x 5 (21, 0) (1, 2) x 5 0 22, 7 2 2 2 7 4 , 1 2 49. Step 1: ( ) = + f x x x 1 4 3 ; domain: { } ≠ x x 0 Step 2: f is in lowest terms Step 3: no y-intercept; no x-intercepts Step 4: f is in lowest terms; vertical asymptote: = x 0 Step 5: Oblique asymptote: = y x, not intersected Step 6: 5 25 25 5 Step 7: y 5 x 5 (21, 22) (1, 2) x 5 0 y 5 x 51. One possibility: ( ) = − R x x x 4 2 2 53. One possibility: ( ) ( ) ( )( ) ( ) ( ) = − − + + − R x x x x x x 1 3 4 3 1 2 2 2 2 55. P(x) x 1 0 1020 405060 30 The likelihood of your ball being chosen decreases very quickly and approaches 0 as the number of attendees, x, increases. 57. (a) t-axis; ( ) → C t 0 (b) 0.4 0 0 12 (c) 0.71 h after injection 59. (a) ( ) = + + C x x x 16 5000 100 (b) > x 0 (c) 10,000 0 0 300 (d) Approximately 17.7 ft by 56.6 ft (longer side parallel to river) 61. (a) ( ) = + S x x x 2 40,000 2 (b) 10,000 0 0 60 (c) 2784.95 in.2 (d) × × 21.54 in. 21.54 in. 21.54 in. (e) To minimize the cost of materials needed for construction 63. (a) π ( ) = + C r r r 12 4000 2 (b) 6000 0 0 10 The cost is smallest when = r 3.76 cm. 65. (a) 0.8126 (b) 0.7759; a player serving, with probability 0.62 of winning a point on a serve, has probability 0.7759 of winning the game. (c) ≈ x 0.7 (d) 0 1 1 67. (a) ( ) = + − − − ≠ = ⎧ ⎨ ⎪⎪ ⎪⎪⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ R x x x x x x x 12 6 if 3 7 5 if 3 2 2 (b) ( ) = − − − + ≠ − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ R x x x x x x x 6 7 3 2 7 6 if 3 2 11 if 3 2 2 2 69. No. Each function is a quotient of polynomials, but it is not written in lowest terms. Each function is undefined for = x 1; each graph has a hole at = x 1. 75. If there is a common factor between the numerator and the denominator, then the graph will have a hole. 76. − + − x x x 4 5 2 2 3 2 77. { } − 1 10 78. 17 2 79. ( ) +x 2 1 2 80. = − y x 4 81. ( ) = g 3 6 82. − − x x 4 2 83. perpendicular 84. { }9 85. { } − 2, 2 4.7 Assess Your Understanding (page 263) 3. c 4. F 5. (a) { } ( ) ( ) < < > ∪ ∞ x x x 0 1 or 2 ; 0,1 2, (b) { } ( ] [ ] ≤ ≤ ≤ −∞ ∪ x x x 0 or 1 2 ; , 0 1, 2 7. (a) { } ( ) ( ) − < < > − ∪ ∞ x x x 1 0 or 1 ; 1, 0 1, (b) { } ( ) [ ) < − ≤ < −∞ − ∪ x x x 1 or 0 1 ; , 1 0, 1 9. { } ( ) ( ) < < < −∞ ∪ x x x 0 or 0 3 ; , 0 0, 3 11. { } ( ] ≤ −∞ x x 1 ; , 1 13. { } ( ] [ ) ≤ − ≥ −∞ − ∪ ∞ x x x 2 or 2 ; , 2 2, 15. { } ( ) ( ) − < < − > − − ∪ ∞ x x x 4 1 or 0; 4, 1 0, 17. { } ( ] − < ≤ − − − x x 2 1; 2, 1 19. { } ( ) < − −∞ − x x 6 ; , 6 21. { } ( ) > ∞ x x 4; 4, 23. { } ( ) ( ) − < < > − ∪ ∞ x x x 4 0 or 0 ; 4, 0 0, 25. { } ( ] [ ] ≤ − ≤ ≤ −∞ − ∪ x x x 2 or 4 6 ; , 2 4, 6
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