AN14 Answers: Chapter 3 49. (a) ( ) = + C x x 90 1800 (b) C(x) x 1000 2000 3000 0 4 8 12 Cost (dollars) Number of Bicycles (c) $3060 (d) 22 bicycles 51. (a) ( ) = d w w 5.5 (b) 13.2 cm (c) 3.6 kg (b) Since each input (soda) corresponds to a single output (hot dogs), we know that number of hot dogs purchased is a function of number of sodas purchased. Also, because the average rate of change is a constant −0.6 hot dog per soda, the function is linear. 53. (a) h s 4 8 0 10 20 Hot Dogs Sodas (d) { } [ ] ≤ ≤ s s 0 20 or 0, 20 (e) h s 4 8 0 10 20 Hot Dogs Sodas (f) If the number of sodas purchased increases by 1, the number of hot dogs purchased decreases by 0.6. (g) h-intercept: If 0 sodas are purchased, then 12 hot dogs may be purchased. s-intercept: If 0 hot dogs are purchased, then 20 sodas can be purchased. 55. d, e 57. ( ) = = b f x b 0; yes, 59. y x (2, 5) 2 10 60. 6 61. 7 62. y x ( 1, 1) ( 2, 4) (1, 2) (4, 3) 5 5 63. ( ) ( ) = − − f x x 5 18 2 64. ( ) ( ) = + − g x x 3 5 2 23 4 2 65. x-intercepts: −3 2, 3 2; y-intercept: 8 66. x x x 2, 4 { } ≥− ≠ 67. = − + y x2 9 68. –2 –40 40 8 Local maximum: ( ) = f 1 4 Local minimum: ( ) = − f 4.33 14.52 Increasing: [ ] [ ] − ∪ 2, 1 4.33, 8 Decreasing: [ ] 1, 4.33 3.2 Assess Your Understanding (page 153) 3. scatter plot 4. T 5. Linear relation, > m 0 7. Linear relation, < m 0 9. Nonlinear relation 11. (a) y x 8 16 4 8 (b) Answers will vary. Using ( ) 4,6 and ( ) 8, 14 , = − y x2 2. (c) y x 8 16 4 8 (4, 6) (8, 14) (d) = − y x 2.0357 2.3571 (e) ≈ r 0.996 (f) 20 0 0 10 13. (a) y x 22 25 2 5 (b) Answers will vary. Using ( ) − − 2, 4 and ( ) 2, 5 , = + y x 9 4 1 2 . (c) y x (2, 5) (22, 24) 25 2 5 22 (d) = + y x 2.2 1.2 (e) ≈ r 0.976 (f) 6 23 26 3 15. (a) y x 100 140 210 220 (b) Answers will vary. Using ( ) ( ) − − = + y x 20, 100 and 10, 140 , 4 180. (c) (220, 100) (210, 140) y x 100 140 210 220 (d) = + y x 3.8613 180.2920 (e) ≈ r 0.957 (f) 150 0 90 225 17. (a) x 280 260 240 220 200 38 Number of Calories Weight (grams) 46 5462 70 (b) Linear with positive slope (c) Answers will vary. Using the points ( ) 39.52, 210 and ( ) 66.45, 280 , = + y x 2.599 107.288. (d) y x 280 260 240 220 200 38 Number of Calories Weight (grams) 465462 70 (e) 269 calories (f) If the weight of a candy bar is increased by 1 gram, the number of calories will increase by 2.599, on average.
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