Section 4.5 AN25 35. ( ) ( )( )( ) − + = − − + − − i i f x x x i x i 2, 3 2, 3 2; 2 3 2 3 2 37. ( ) ( )( )( )( ) − − = + − + − i i i i f x x i x i x i x i , , 2, 2; 2 2 39. ( ) ( )( )( )( ) − − = + − + − i i f x x i x i x x 5, 5, 3, 1; 5 5 3 1 41. ( ) ( ) ( ) ( )( ) − − + = + − − + − − i i f x x x x i x i 4, 1 3 ,2 3,2 3; 3 4 1 3 2 3 2 3 43. 130 45. (a) ( )( ) ( ) = − + + + f x x x x x 2 1 2 1 2 2 (b) − − − + − + i i i i 2 2 2 2 , 2 2 2 2 , 2 2 2 2 , 2 2 2 2 47. Zeros that are complex numbers must occur in conjugate pairs; or a polynomial with real coefficients of odd degree must have at least one real zero. 49. If the remaining zero were a complex number, its conjugate would also be a zero, creating a polynomial of degree 5. 51. y 7 −5 −2 x 10 52. −22 53. − − + x x x 6 13 13 20 3 2 54. π π ( ) ( ) = ≈ = ≈ A C 9 ft 28.274 ft ; 6 ft 18.850 ft 2 2 55. ( )( ) ( ) = − + g f x x x x 3 2 1 ; Domain: ≠ − x 1 and ≠ x 0 56. ( ) = + − y x 5 3 2 57. [ )∞ 0, 58. ( ) ( ) ( ) − 0, 2 3, 0,2 3, 4,0 59. ( ) ( ) − + + x x x 9 7 3 60. + + x xh h 3 3 2 2 39. (a) y 2 x 4 (21, 21) (23, 21) x 5 22 y 5 0 4.5 Assess Your Understanding (page 244) 5. (a) = − = x x 2; 1 (b) odd; even (c) odd; even 6. F 7. horizontal asymptote 8. vertical asymptote 9. T 10. F 11. = y 0 12. T 13. d 14. a 15. All real numbers except 7; { } ≠ x x 7 17. All real numbers except 2 and { } − ≠ ≠ − x x x 4; 2, 4 19. All real numbers except { } − ≠ − ≠ x x x 3 2 and 4; 3 2 , 4 21. All real numbers except 4; { } ≠ x x 4 23. All real numbers 25. All real numbers except { } − ≠ − ≠ x x x 2 and 2; 2, 2 27. (a) Domain: { } { } ≠ ≠ x x y y 2 ; range: 1 (b) ( ) 0, 0 (c) = y 1 (d) = x 2 (e) None 29. (a) Domain: { } ≠ x x 0 ; range: all real numbers (b) ( ) ( ) −1, 0 , 1, 0 (c) None (d) = x 0 (e) = y x2 31. (a) Domain: { } { } ≠ − ≠ ≤ > x x x y y y 2, 2 ; range: 0, 1 (b) ( ) 0, 0 (c) = y 1 (d) = − = x x 2, 2 (e) None 33. (a) y 8 x 5 (21, 1) (1, 3) y 5 2 x 5 0 (b) Domain: { } ≠ x x 0 ; range: { } ≠ y y 2 (c) Vertical asymptote: = x 0; horizontal asymptote: = y 2 35.(a) y 10 x 5 (0, 1) (2, 1) x 5 1 y 5 0 (b) Domain: { } ≠ x x 1 ; range: { } > y y 0 (c) Vertical asymptote: = x 1; horizontal asymptote: = y 0 (b) Domain: { } ≠ − x x 1 ; range: { } ≠ y y 0 (c) Vertical asymptote: = − x 1; horizontal asymptote: = y 0 37. (a) y 5 x 5 (22, 2) (1, 21) x 5 21 y 5 0 (b) Domain: { } ≠ − x x 2 ; range: { } < y y 0 (c) Vertical asymptote: = − x 2; horizontal asymptote: = y 0 41. (a) y 10 x 9 (4, 3) (2, 3) x 5 3 y 5 1 (b) Domain: { } ≠ x x 3 ; range: { } > y y 1 (c) Vertical asymptote: = x 3; horizontal asymptote: = y 1 43. (a) y 3 x 5 (22, 0) (2, 0) x 5 0 y 5 1 (b) Domain: { } ≠ x x 0 ; range: { } < y y 1 (c) Vertical asymptote: = x 0; horizontal asymptote: = y 1 45. Vertical asymptote: = − x 4; horizontal asymptote: = y 3 47. Vertical asymptote: = x 3; oblique asymptote: = + y x 5 49. Vertical asymptotes: = = − x x 1, 1; horizontal asymptote: = y 0 51. Vertical asymptote: = − x 1 3 ; horizontal asymptote: = y 2 3 53. Vertical asymptote: none; no horizontal or oblique asymptote 55. Vertical asymptote: = x 0; no horizontal or oblique asymptote 57. (a) 9.8208 m sec2 (b) 9.8195 m sec2 (c) 9.7936 m sec2 (d) h-axis (e) ∅ 59. (a) Rtot R2 5 10 0 5 10152025 (b) Horizontal: = R 10; tot as the resistance of R2 increases without bound, the total resistance approaches 10 ohms, the resistance R .1 (c) ≈ R 103.5 1 ohms 61. (a) ( ) ( ) = + − = − + R x x x 2 5 1 5 1 1 2 (b) y x 10 210 5 25 x 5 1 y 5 2 y 5 2 (0, 23) (2, 7) (c) Vertical asymptote: = x 1; horizontal asymptote: = y 2 67. = x 5 68. { } − 4 19 69. x-axis symmetry 70. ( ) ( ) − − 3,11 , 2, 4 71. ( ) ( ) − 6,0, 0, 3 72. ( ) − = f 3 19 73. ( ) − 2 5 , 3 74. Odd 75. − − x x 9 2 9 2 76. − 9 7
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