Section 3.1 AN13 Cumulative Review (page 136) 1. { }6 2. { } 0, 1 3 3. { } −1, 9 4. { } 1 3 , 1 2 5. { } − 7 2 , 1 2 6. { } 1 2 7. { } ( ) < − −∞ − x x 4 3 ; , 4 3 8. { } ( ) < < x x 1 4 ; 1, 4 9. { } ) ( ] ≤ − ≥ −∞ − ∪ ⎡ ∞ ⎣ ⎢ x x x 2 or 3 2 ; , 2 3 2 , 7. (a) y x 3 5 (b) 0, 4, 4,0 ( ) ( ) − (c) ( ) − = − g 5 9 (d) ( ) = − g 2 2 8. (a) 18 (b) = − y x 18 32 9. (a) ( )( ) − = − + f g x x x 2 3 3 2 (b) ( )( ) ⋅ = − + − f g x x x x 6 4 3 2 3 2 (c) ( ) ( ) + − = + f x h f x xh h 4 2 2 10. (a) (0, 1) (21, 3) (22, 5) y x 10 2.5 (b) (22, 4) (24, 2) (26, 4) y x 10 10 11. + − x h 2 3 12. (a) π ( ) = − + V x x x x 3 10 3 24 2 2 (b) 3460.29 ft3 13. Even 10. (a) distance: 29 (b) midpoint: ( ) − 1 2 , 4 (c) slope: − 2 5 11. y 3 x 7 (0, 6) (4, 0) 12. y 5 x 5 (1, 1) (4, 2) (1, 1) (0, 0) (4, 2) 13. y 8 x 5 (0, 1) ( 4, 3) (0, 7) (4, 3) (0, 3) 14. y 5 x 5 (4, 2) (1, 1) (0, 0) 15. Intercepts: 0, 3 , 2, 0 , ( ) ( ) − − ( ) 2, 0 ; symmetry with respect to the y-axis 16. = + y x 1 2 5 17. y 5 x 5 ( 4, 1) (2, 3) (0, 1) 18. y 5 x 5 (1, 1) 1 3 3, 1 2 2, 19. y 5 x 5 (4, 4) (2, 0) (0, 2) 4 3 1 4 2 3 2 19. (a) = = m b 0; 4 (b) y x (0, 4) 5 5 (c) 0 (d) Constant 21. Linear; −3 23. Nonlinear 25. Nonlinear 27. Linear; 0 CHAPTER 3 Linear and Quadratic Functions 3.1 Assess Your Understanding (page 145) 7. slope; y-intercept 8. positive 9. T 10. F 11. a 12. d 13. (a) = = m b 2; 3 (b) y x (1, 5) 2 1 (0, 3) 8 8 (c) 2 (d) Increasing 15. (a) = − = m b 3; 4 (b) y x (0, 4) (1, 1) 3 1 8 8 (c) −3 (d) Decreasing 17. (a) = = − m b 1 4 ; 3 (b) y x 1 (4, 2) (0, 3) 4 5 8 (c) 1 4 (d) Increasing 29. (a) 1 4 (b) { } ( ) > ∞ x x 1 4 or 1 4 , (c) 1 (d) { } ( ] ≤ −∞ x x 1 or , 1 (e) y x (1, 3) y g(x) y f(x) 4 5 31. (a) 40 (b) 88 (c) −40 (d) { } > x x 40 or ( )∞ 40, (e) { } ≤ x x 88 or ( ] −∞, 88 (f) { } − < < x x 40 88 or ( ) −40, 88 33. (a) −4 (b) { } <− x x 4 or ( ) −∞ −, 4 35. (a) −6 (b) { } − ≤ < x x 6 5 or [ ) −6, 5 37. (a) $185 (b) 64 mi (c) 26 mi (d) { } [ ) ≥ ∞ x x 0 or 0, 39. (a) 410.5 minutes (b) 8:24 am 41. (a) $24; 600 T-shirts (b) ≤ < p $0 $24 (c) The price will increase. 43. (a) ( ] < ≤ x 11,600 47,150 or 11 600, 47 150 (b) $2168 (c) The taxable income, x, is the independent variable. The tax bill, T, is the dependent variable. (d) T 2000 4000 6000 x (11 600, 1160) 0 10,000 40,000 (47 150, 5426) (e) $28,125 45. (a) = x 5000 (b) > x 5000 47. (a) ( ) = − + V x x 1000 3000 (b) { } [ ] ≤ ≤ x x 0 3 or 0, 3 (c) V(x) x 1000 2000 0 1 2 Book Value (dollars) Age 3000 3 (d) $1000 (e) After 1 year
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