AN32 Answers: Chapter 4 41. Step 1: Domain: { } ≠ x x 1 Step 2: R is in lowest terms Step 3: y-intercept: 0; x-intercept: 0 Step 4: R is in lowest terms; vertical asymptote: = x 1 Step 5: No oblique or horizontal asymptote Step 6: 60 24 25 4 Step 7: y 40 x 5 (0, 0) (2, 32) 22, 32 9 , 1 2 1 2 x 5 1 42. Step 1: ( ) ( )( ) ( )( ) = + − + − G x x x x x 2 2 1 2 ; domain: { } ≠ − ≠ x x x 1, 2 Step 2: In lowest terms, ( ) = + + G x x x 2 1 Step 3: y-intercept: 2; x-intercept: −2 Step 4: Vertical asymptote: = − x 1; hole at ( ) 2, 4 3 Step 5: Horizontal asymptote: = y 1, not intersected Step 6: 6 24 26 8 Step 7: y 5 x 5 (0, 2) (22, 0) 3, 5 4 2, 4 3 23, 1 2 x 5 21 y 5 1 2 3 2 , 21 43. (a) { } −3, 2 (b) ( ) ( ) − ∪ ∞ 3, 2 2, (c) ( ] { } −∞ − ∪ , 3 2 (d) ( ) ( ) ( ) = − + f x x x 2 3 2 44. (a) = y 0.25 (b) = − = x x 2, 2 (c) ( ) ( ) − − ∪ − 3, 2 1, 2 (d) ( ] ( ] ( ) −∞ − ∪ − − ∪ ∞ , 3 2, 1 2, (e) ( ) = + + − R x x x x 4 3 4 16 2 2 45. { } ( ) ( ) <− −< < −∞− ∪− x x x 2 or 1 2 ; , 2 1, 2 22 2 21 46. { } [ ] [ ) − ≤ ≤ − ≥ − − ∪ ∞ x x x 4 1 or 1; 4, 1 1, 1 21 24 47. { } ( ) ( ) < > −∞ ∪ ∞ x x x 1 or 2 ; , 1 2, 1 2 48. { } [ ] ( ) ≤ ≤ > ∪ ∞ x x x 1 2 or 3 ; 1,2 3, 3 2 1 49. { } ( ) ( ) ( ) <− << > −∞−∪ ∪∞ x x x x 4 or 2 4 or 6 ; , 4 2,4 6, 24 2 4 6 50. (a) π ( ) = + A r r r 2 500 2 (b) 223.22 cm2 (c) 257.08 cm2 (d) 1000 0 0 8 A is smallest when ≈ r 3.41cm. 51. (a) 0 8 460 270 The relation appears to be cubic. (b) ( ) = − + + P t t t t 2.206 21.346 67.698 250.486; $555.4 3 2 (c) 0 8 460 270 Chapter Test (page 269) 1. y 7 x 8 (4, 21) (2, 21) (3, 22) 2. (a) 3 (b) ± ± ± ± ± ± ± ± p q : 1 2 , 1, 3 2 , 5 2 , 3, 5, 15 2 , 15 (c) ( ) ( )( )( ) − − = + + − g x x x x 5, 1 2 , 3; 5 2 1 3 (d) y-intercept: −15; x-intercepts: − − 5, 1 2 , 3 (e) Crosses at − − 5, 1 2 , 3 (f) = y x2 3 (g) ( ) ( ) − − 3.15, 60.30 , 1.48, 39.00 (h) y 60 x 5 (3, 0) (1.48, 239.00) (0, 215) 0 2 , 1 2 (23.15, 60.30) (22, 45) (25, 0)
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