AN18 Answers: Chapter 3 46. (a) ( ) 9,0, 0, 6 ( ) − (b) y x (0, 6) (9, 0) 5 5 47. = d t 58 48. 3 17, 3 17 { } − − − + 49. ( ) 0, 25 , ( ) ( ) − 5 2 , 0 , 5 2 , 0 50. − + + x x 3 2 51. + − + x x x 3 2 29 28 3 2 52. + − x h 6 3 5 53. ( ) ( ) + + x x x 2 35 2 7 4 5 or ( ) + + x x x 2 35 2 7 5 4 5 14. Minimum value; 1 15. Maximum value; 12 16. Maximum value; 16 17. x x 8 2 ; 8, 2 { } ( ) − < < − 18. x x x 1 3 or 5 ; , 1 3 5, { } ( [ ) ≤− ≥ −∞ − ⎤ ⎦ ⎥ ∪ ∞ 19. y x x 3 12 16 2 = − + − 20. y x x2 3 2 = + + 21. (a) S x x 0.01 25,000 ( ) = + (b) $35,000 (c) $7,500,000 (d) > x $12,500,000 22. (a) ( ) = − + R p p p 10 1500 2 (b) { } ≤ ≤ p p 0 150 (c) $75 (d) $56,250 (e) 750 units (f) Between $70 and $80 23. 50 ft by 50 ft 24. 4,166,666.7 m2 25. The side with the semicircles should be π 50 ft; the other side should be 25 ft. 26. (a) 63 clubs (b) $151.90 27. ( ) = − + A x x x 10 ; 25 sq. units 2 28. 3.6 ft Review Exercises (page 184) 1. (a) = = − m b 2; 5 (b) 2 (c) y x (0, 5) (1, 3) , 0 5 2 2 5 (d) Increasing 2. (a) = = − m b 4 5 ; 6 (b) 4 5 (c) y x (0, 6) (5, 2) , 0 15 2 2 8 (d) Increasing 3. (a) = = m b 0; 4 (b) 0 (c) x (0, 4) (4, 4) ( 3, 4) 5 5 (d) Constant 4. Linear; Slope: 5 5. Nonlinear 6. y x (22, 23) (21, 24) (0, 23) 5 5 7. y x (5, 1) (3, 1) (4, 0) 5 8 8. y x ( 2, 1) (3, 2) (1, 2) 5 5 9. (a) y x (2, 2) (4, 6) (0, 6) x 2 8 8 (b) Domain: ( ) −∞ ∞, Range: [ )∞ 2, (c) Decreasing: ( ] −∞, 2 Increasing: [ )∞ 2, 10. (a) y x (8, 0) (0, 16) ( 8, 0) 2 10 (b) Domain: ( ) −∞∞, Range: 16 [ ) − ∞ (c) Decreasing: ( ] −∞, 0 Increasing: [ )∞ 0, 11. (a) y x (1, 0) (0, 0) 1 2 , 1 x 1 2 2.5 2.5 (b) Domain: ( ) −∞∞, Range: ( ] −∞, 1 (c) Increasing: (−∞ ⎤ ⎦ ⎥ , 1 2 Decreasing: 1 2 , ) ⎡ ∞ ⎣ ⎢ 12. (a) y x (0, 1) 1 , 3 1 2 x 1 3 2.5 2.5 (b) Domain: ( ) −∞ ∞, Range: ) ⎡ ∞ ⎣ ⎢ 1 2 , (c) Decreasing: (−∞ − ⎤ ⎦ ⎥ , 1 3 Increasing: 1 3 , ) ⎡ − ∞ ⎣ ⎢ 13. (a) y x (0.22, 0) ( 1.55, 0) (0, 1) x 2 3 2 , 3 7 3 5 5 (b) Domain: ( ) −∞ ∞, Range: 7 3 , ) ⎡ − ∞ ⎣ ⎢ (c) Decreasing: (−∞ − ⎤ ⎦ ⎥ , 2 3 Increasing: 2 3 , ) ⎡ − ∞ ⎣ ⎢ 29. (a) y 38 37 36 35 34 24 Tibia (mm) Humerus (mm) 25 262728 x (b) yes (c) = + y x 1.3902 1.1140 (d) 37.95 mm 30. (a) Quadratic, < a 0 6500 6400 6300 6200 6100 20 Total Revenue (thousands of dollars) Advertising (thousands of dollars) 25 30 (b) About $26.5 thousand (c) $6408 thousand (e) 6500 15 6000 35 Chapter Test (page 186) 1. (a) Slope: −4; y-intercept: 3 (b) −4 (c) Decreasing (d) y x (0, 3) (1, 1) 5 5 2. ( ) ( ) ( ) − − 4 3 ,0, 2,0, 0, 8 3. ( ) ⎛ − ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ ⎛ + ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 2 6 2 , 0 , 2 6 2 , 0 , 0, 1 4. (a) { } −1, 3 (b) y x (0, 0) (3, 18) (1, 2) ( 3, 0) 4 21 (c) { } ( ) − < < − x x 1 3 ; 1, 3 5. y x (0, 7) (6, 7) (2, 1) (4, 1) (3, 2) 9 8 –6–5–4–3–2–1 0 1 2 3 4 5 6 6. (a) Concave up (b) ( ) − 2, 8 (c) = x 2 (d) x-intercepts: − + 6 2 6 3 , 6 2 6 3 ; y-intercept: 4 (e) y x (2, 8) x 2 (0, 4) (4, 4) (0.37, 0) (3.63, 0) 10 10 7. Maximum value; 21 8. { } ] [ ( ) ≤ ≥ −∞ ∪ ∞ x x x 4 or 6 ; , 4 6, 9. (a) ( ) = + C m m 0.15 129.50 (b) $258.50 (c) 562 miles 10. (a) ( ) = − + R p p p 10 10,000 2 (b) p p 0 1000 { } ≤ ≤ (c) $500 (d) $2,500,000 (e) 5000 (f) Between $200 and $800
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