Section 2.3 AN7 111. (a) $222 (b) $225 (c) $220 (d) $230 113. ( ) ( ) ( ) = R x L x P x 115. ( ) ( ) ( ) = ⋅ H x P x I x 117. (a) ( ) = − + + − P x x x x 0.05 0.8 155 500 3 2 (b) ( ) = P 15 $1836.25 (c) When 15 hundred smartphones are sold, the profit is $1836.25. 119. (a) ( ) = + − D v v v 0.05 2.6 15 2 (b) 321 feet (c) The car will need 321 feet to stop once the impediment is observed. 121. ( ) ( ) + + + + x h x x h x 1 2 3 1 3 1 3 2 3 123. { } − < < x x 2 8 3 125. ( ) = − H x x x 3 age 3 127. Intercepts: ( ) ( ) − − 16, 0 , 8, 0 ; x-axis symmetry 128. ( ) 4, 32 129. 7.5 lbs 130. { } −3, 2, 3 131. = − − a d bx c 1 or = − − a bx d c 1 132. ⋅ 2.5 kg m2 133. − 10 3 134. ( ) − + + − x x x 12 40 21 4 7 2 2 2 135. 7 2.2 Assess Your Understanding (page 81) 3. vertical 4. − 5; 3 5. = − a 2 6. F 7. F 8. T 9. c 10. a 11. (a) ( ) ( ) = − = − f f 0 3; 6 3 (b) ( ) ( ) = = f f 6 0; 11 1 (c) Positive (d) Negative (e) −3, 6, and 10 (f) − < < < ≤ x x 3 6; 10 11 (g) { } − ≤ ≤ x x 6 11 (h) { } − ≤ ≤ y y 3 4 (i) −3, 6, 10 (j) 3 (k) 3 times (l) Once (m) 0, 4 (n) −5, 8 13. Not a function (a) Domain: { } ≤ − ≥ x x x 1 or 1 ; Range: all real numbers (b) ( ) ( ) −1, 0 , 1, 0 (c) x-axis, y-axis, and origin symmetry 15. Function (a) Domain: π π { } − ≤ ≤ x x ; Range: { } − ≤ ≤ y y 1 1 (b) π π ( ) ( ) ( ) − 2 , 0 , 2 ,0 , 0,1 (c) y-axis 17. Not a function (a) Domain: { } ≤ x x 0 ; Range: all real numbers (b) ( ) 0, 0 (c) x-axis 19. Function (a) Domain: { } < < x x 0 3 ; Range: { } < y y 2 (b) ( ) 1, 0 (c) None 21. Function (a) Domain: all real numbers; Range: { } ≤ y y 2 (b) ( ) −3, 0 , ( ) 3, 0 , ( ) 0, 2 (c) y-axis 23. Function (a) Domain: all real numbers; Range: { } ≥ − y y 3 (b) ( ) 1, 0 , ( ) 3, 0 , ( ) 0, 9 (c) None 25. (a) Yes (b) ( ) ( ) − = − f 2 8; 2, 8 (c) ( ) ( ) − − − − 0 or 1 3 ; 0, 2, 1 3 , 2 (d) All real numbers (e) −1, 2 3 (f) −2 27. (a) No (b) ( ) ( ) = − − f 4 3; 4, 3 (c) 14; ( ) 14, 2 (d) { } ≠ x x 6 (e) −2 (f) − 1 3 29. (a) Yes (b) ( ) ( ) = f 3 486 5 ; 3, 486 5 (c) − − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 3 3 or 3 3 ; 3 3 , 1 , 3 3 , 1 (d) All real numbers (e) 0 (f) 0 31. (a) 3 (b) −2 (c) −1 (d) 1 (e) 2 (f) − 1 3 33. (a) Approximately 10.4 ft high (b) Approximately 9.9 ft high (c) h x 10 5 0 5 10152025 (8, 10.4) (12, 9.9) (22.6, 0) (20, 3.6) (15, 8.4) (0, 6) (d) The ball will not go through the hoop; ( ) ≈ h 15 8.4 ft. If ( ) = = v h 30 ft sec, 15 10 ft. 35. (a) About 81.07 ft (b) About 129.59 ft (c) About 26.63 ft; The ball is about 26.63 feet high after it has traveled 500 feet. (d) About 528.13 ft (e) 150 0 0 550 (f) About 115.07 ft and 413.05 ft (g) 275 ft; maximum height shown in the table is 131.8 ft (h) 264 ft 37. (a) $223; $220 (b) { } > x x 0 (c) 500 0 0 1000 (d) (e) 600 mi h 39. (a) $50; It costs $50 if you use 0 gigabytes. (b) $50; It costs $50 if you use 5 gigabytes. (c) $150; It costs $150 if you use 15 gigabytes. (d) { } ≤ ≤ g g 0 30 . There are at most 30 gigabytes used in a month. 41. 420 43. The x-intercepts can number anywhere from 0 to infinitely many. There is at most one y-intercept. 45. (a) III (b) IV (c) I (d) V (e) II 47. y x 5 4 3 2 1 0 10 20 Distance (blocks) Time (minutes) (5, 2) (7, 0) (6, 0) (22, 5) (29, 0) 49. (a) 2 hr elapsed during which Sobia was between 0 and 3 mi from home (b) 0.5 hr elapsed during which Sobia was 3 mi from home (c) 0.3 hr elapsed during which Sobia was between 0 and 3 mi from home (d) 0.2 hr elapsed during which Sobia was 0 mi from home (e) 0.9 hr elapsed during which Sobia was between 0 and 2.8 mi from home (f) 0.3 hr elapsed during which Sobia was 2.8 mi from home (g) 1.1 hr elapsed during which Sobia was between 0 and 2.8 mi from home (h) 3 mi (i) Twice 51. No points whose x-coordinate is 5 or whose y-coordinate is 0 can be on the graph. 54. − + − x x5 9 2 55. 2 10 56. = + y x 2 3 8 57. All real numbers or ( ) −∞∞, 58. 36 59. + x 1 6 60. 55.8 min 61. { } − < ≤ x x 4 1 or ( ] −4, 1 62. − + x x 5 15 12 2 63. [ ] −3, 10 2.3 Assess Your Understanding (page 95) 6. increasing 7. even; odd 8. T 9. T 10. F 11. c 12. d 13. Yes 15. No 17. [ ] [ ] [ ] − − 8, 2; 0,2; 5,7 19. Yes; 10 21. −2, 2; 6, 10 23. ( ) − = − f 8 4 25. (a) ( ) −2, 0 , ( ) 0, 3 , ( ) 2, 0 (b) Domain: { } − ≤ ≤ x x 4 4 or [ ] −4, 4 ; Range: { } ≤ ≤ y y 0 3 or [ ] 0, 3 (c) Increasing on [ ] −2, 0 and [ ] 2, 4 ; Decreasing on [ ] − − 4, 2 and [ ] 0, 2 (d) Even 27. (a) ( ) 0, 1 (b) Domain: all real numbers; Range: { } > y y 0 or ( )∞ 0, (c) Increasing on ( ) −∞∞, (d) Neither 29. (a) π π ( ) ( ) ( ) − ,0, 0,0, ,0 (b) Domain: π π { } − ≤ ≤ x x or π π [ ] − , ; Range: { } − ≤ ≤ y y 1 1 or [ ] −1, 1 (c) Increasing on π π ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ 2 , 2 ; Decreasing on π π ⎡ − − ⎣ ⎢ ⎤ ⎦ ⎥ , 2 and π π ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 2 , (d) Odd 31. (a) ( ) ( ) ( ) 0, 1 2 , 1 3 , 0 , 5 2 , 0
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