AN6 Answers: Chapter 2 7. (a) = − m 2 3 (b) For every 3-unit change in x, y will change by −2 units. 8. y 5 x 10 (9, 3) (4, 2) (1, 1) (0, 0) (1, 21) (4, 22) (9, 23) 9. Intercepts: ( ) ( ) ( ) −3, 0 , 3, 0 , 0, 9 ; symmetric with respect to the y-axis 10. = − + y x2 2 y 5 x 5 (0, 2) (1, 0) (3, 24) 11. + − + = x y x y 8 6 0 2 2 12. Center: ( ) −2, 1 ; radius: 3 y 5 x 4 (22, 1) 13. Parallel line: = − − y x 2 3 1 3 ; perpendicular line: = + y x 3 2 3 CHAPTER 2 Functions and Their Graphs 2.1 Assess Your Understanding (page 73) 7. independent; dependent 8. a 9. c 10. F 11. F 12. verbally; numerically; graphically; algebraically 13. F 14. F 15. difference quotient 16. explicitly 17. (a) Domain: { } 0, 22, 40, 70, 100 in °C Range { } 1.031, 1.121, 1.229, 1.305, 1.411 in kg m3 (b) Temperature, 8C 0 22 40 100 70 1.411 1.305 1.229 1.121 1.031 Density, kg/m3 (c) ( ) ( ) ( ) ( ) ( ) { } 0, 1.411 , 22, 1.305 , 40, 1.229 , 70, 1.121 , 100, 1.031 19. Domain: { } Elvis, Colleen, Kaleigh, Marissa ; Range: { } January 8, March 15, September 17 ; Function 21. Domain: { } 20, 30, 40 ; Range: { } 300, 350, 540, 880 ; Not a function 23. Domain: { } −3, 2, 4 ; Range: { } 6, 9, 10 ; Not a function 25. Domain: { } 1, 2, 3, 4 ; Range: { }3 ; Function 27. Domain: { } −4, 0, 3 ; Range: { } 1, 3, 5, 6 ; Not a function 29. Domain: { } −1, 0, 2, 4 ; Range: { } −1, 3, 8 ; Function 31. Function 33. Function 35. Not a function 37. Not a function 39. Function 41. Not a function 43. (a) −4 (b) 1 (c) −3 (d) − − x x 3 2 4 2 (e) − − + x x 3 2 4 2 (f) + + x x 3 8 1 2 (g) + − x x 12 4 4 2 (h) + + + + − x xh h x h 3 6 3 2 2 4 2 2 45. (a) 0 (b) 1 2 (c) − 1 2 (d) − + x x 1 2 (e) − + x x 1 2 (f) + + + x x x 1 2 2 2 (g) + x x 2 4 1 2 (h) + + + + x h x xh h 2 1 2 2 47. (a) 4 (b) 5 (c) 5 (d) + x 4 (e) − − x 4 (f) + + x 1 4 (g) + x 2 4 (h) + + x h 4 49. (a) − 1 5 (b) − 3 2 (c) 1 8 (d) − + x x 2 1 3 5 (e) − − − x x 2 1 3 5 (f) + − x x 2 3 3 2 (g) + − x x 4 1 6 5 (h) + + + − x h x h 2 2 1 3 3 5 51. All real numbers 53. All real numbers 55. { } ≠ − ≠ x x x 4, 4 57. { } ≠ x x 0 59. { } ≥ x x 4 61. { } ≠ − − x x 2, 1 63. { } > x x 4 65. { } ≥ ≠ t t t 4, 7 67. All real numbers 69. { } ≠ − ≠ t t t 2, 7 71. (a) ( )( ) + = + f g x x5 1; All real numbers (b) ( )( ) − = + f g x x 7; All real numbers (c) ( )( ) ⋅ = − − f g x x x 6 12; 2 All real numbers (d) { } ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = + − ≠ f g x x x x x 3 4 2 3 ; 3 2 (e) 16 (f) 11 (g) 10 (h) −7 73. (a) ( )( ) + = + − f g x x x 2 1; 2 All real numbers (b) ( )( ) − = − + − f g x x x 2 1; 2 All real numbers (c) ( )( ) ⋅ = − f g x x x 2 2 ; 3 2 All real numbers (d) ( ) { } ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = − ≠ f g x x x x x 1 2 ; 0 2 (e) 20 (f) −29 (g) 8 (h) 0 75. (a) ( )( ) { } + = + − ≥ f g x x x x x 3 5; 0 (b) ( )( ) { } − = − + ≥ f g x x x x x 3 5; 0 (c) ( )( ) { } ⋅ = − ≥ f g x x x x x x 3 5 ; 0 (d) { } ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = − ≥ ≠ f g x x x x x x 3 5 ; 0, 5 3 (e) +3 4 (f) −5 (g) 2 (h) − 1 2 77. (a) ( )( ) { } + = + ≠ f g x x x x 1 2 ; 0 (b) ( )( ) { } − = ≠ f g x x x 1; 0 (c) ( )( ) { } ⋅ = + ≠ f g x x x x x 1 1 ; 0 2 (d) ( ) { } ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = + ≠ f g x x x x 1; 0 (e) 5 3 (f) 1 (g) 3 4 (h) 2 79. (a) { } ( )( ) + = + − ≠ f g x x x x x 6 3 3 2 ; 2 3 (b) { } ( )( ) − = − + − ≠ f g x x x x x 2 3 3 2 ; 2 3 (c) { } ( )( ) ( ) ⋅ = + − ≠ f g x x x x x x 8 12 3 2 ; 2 3 2 2 (d) { } ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = + ≠ ≠ f g x x x x x x 2 3 4 ; 0, 2 3 (e) 3 (f) − 1 2 (g) 7 2 (h) 5 4 81. ( ) = − g x x 5 7 2 83. 4 85. +x h 2 87. + − x h 2 1 89. ( )( ) − + − − x h x 20 4 4 3 4 3 91. ( )( ) + + + x x h 6 3 3 93. + − + − x h x 1 2 2 95. ( ) − + + x h x x h 2 2 2 97. ( ) − + − + + − x h x h x 2 4 4 2 2 99. { } −2, 4 101. = − A 7 2 103. = − A 4 105. ( ) = A x x 1 2 2 107. ( ) = G x x 16 109. (a) 15.1 m, 14.071 m, 12.944 m (b) 1.01 sec, 1.43 sec, 1.75 sec (c) 2.02 sec
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