Section 3.3 AN15 19. (a) The independent variable is the number of hours spent playing video games, and cumulative grade-point average is the dependent variable because we are using number of hours playing video games to predict (or explain) cumulative gradepoint average. (b) 4 21 0 13 (c) ( ) = − + G h h 0.0942 3.2763 (d) If the number of hours playing video games in a week increases by 1 hour, the cumulative grade-point average decreases 0.09, on average. (e) 2.52 (f) Approximately 9.3 hours 21. y x 50 40 30 20 10 35 Incidence Rate (per 1000) Age of Mother 40 No, the data do not follow a linear pattern. 23. (a) No (b) d s 410 420 430 400 390 380 370 Homerun Distance (feet) Speed off the Bat (mph) 100 104 108 25. = + = y x r 1.5 3.5; 1 27. No candy bar weighs 0 grams. 29. + = = − + x y y x 2 3 or 2 3 30. x x x 5, 5 { } ≠ − ≠ 31. ( )( ) − = − + g f x x x8 12 2 32. ( ) = + − y x 3 4 2 33. { } − + 2 7, 2 7 34. ) ⎡ − ∞ ⎣ ⎢ 52 7 , 35. Even 36. x-intercept: 2; y-intercept: − 3 4 37. − + +x 1 6 1 38. x x 7 6 2 1 2 ( ) + + 25. (a) Vertex: ( ) − 3, 2 ; Axis of symmetry: = x 3 (b) Concave up (c) y x 5 –5 5 (3, –2) –5 27. (a) Vertex: ( ) 3, 5 ; Axis of symmetry: = x 3 (b) Concave down (c) x –5 5 5 –5 (3, 5) y 29. (a) Vertex: ( ) 6, 3 ; Axis of symmetry: x 6 = (b) Concave up (c) y x (6, 3) 5 5 31. (a) Vertex: 1 2 , 7 6 ( ) − ; Axis of symmetry: = x 1 2 (b) Concave down (c) 2 y x –5 5 –8 1 2 , 7 6 ( ) – 33. y x 5 5 (4, 4) (2, 1) (0, 0) ( 2, 1) ( 4, 4) 35. y x 5 5 (0, 2) (3, 1) (2, 2) (1, 1) ( 4, 2) 37. ( ) ( ) = + − f x x 2 2 2 y x 5 5 (0, 2) (3, 1) (2, 2) (1, 1) ( 4, 2) 39. ( ) ( ) = − − f x x 2 1 1 2 y x 5 5 (0, 1) (2, 1) (1, 1) 41. ( ) ( ) = − + + f x x 1 1 2 y x 5 5 (0, 0) ( 2, 0) ( 1, 1) 43. ( ) ( ) = + − f x x 1 2 1 3 2 2 y x 5 5 (2, 1) (0, 1) 3 2 1, 45. (a) Vertex: ( ) − − 1, 1 ; Axis of symmetry: = − x 1; Concave up (b) y-intercept: 0; x-intercepts: −2, 0 (c) y x 2 5 (0, 0) (1, 1) ( 2, 0) x 1 (d) Domain: ( ) −∞∞, Range: 1, [ ) − ∞ (e) Decreasing: ( ] −∞ −, 1 Increasing: 1, [ ) − ∞ (f) f x x x 0 on , 2 0, or for 2, 0; ( ) ( ) ( ) > −∞ − ∪ ∞ <− > ( ) ( ) < − − < < f x x 0on 2,0 orfor 2 0 3.3 Assess Your Understanding (page 166) 7. (a) ( ) ( ) = − − g x x 2 3 4 2 (b) ( ) − 1, 3 (c) Down (d) ( ) ( ) = − − − g x x 3 1 3 2 9. parabola 10. axis or axis of symmetry 11. − b a2 12. T 13. T 14. T 15. a 16. d 17. C 19. F 21. G 23. H 47. (a) Vertex: ( ) −3, 9 ; Axis of symmetry: = − x 3; Concave down (b) y-intercept: 0; x-intercepts: −6, 0 (c) y x 9 2 ( 6, 0) ( 3, 9) x 3 (0, 0) (d) Domain: ( ) −∞ ∞, ; Range: ( ] −∞, 9 (e) Increasing: ( ] −∞ −, 3 ; Decreasing: 3, [ ) − ∞ (f) ( ) ( ) ( ) ( ) ( ) > − − < < < −∞ − ∪ ∞ <− > f x x f x x x 0on 6,0 orfor 6 0; 0 on , 6 0, or for 6, 0 49. (a) Vertex: ( ) − − 1, 9 ; Axis of symmetry: = − x 1; Concave up (b) y-intercept: −8; x-intercepts: −4, 2 (c) y x 1 5 ( 4, 0) (0, 8) x 1 (2, 0) (1, 9) (d) Domain: ( ) −∞∞, ; Range: 9, [ ) − ∞ (e) Decreasing: ( ] −∞ −, 1 ; Increasing: 1, [ ) − ∞ (f) f x x x f x x 0on , 4 2, or for 4, 2; 0on 4,2 orfor 4 2 ( ) ( ) ( ) ( ) ( ) > −∞ − ∪ ∞ <− > < − − < < (c) = + d s 3.3641 51.8233 (d) If the speed of the bat increases by 1 mph, the homerun distance increases by 3.3641 feet (e) ( ) = + d s s 3.3641 51.8233 (f) { } > s s 0 (g) Approximately 398 feet
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