3_5 - Chapter 3 Functions and Their Graphs 3.5 1. 3. 5. 7....

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Chapter 3 333 Functions and Their Graphs 3.5 Graphing Techniques; Transformations 1. horizontal, right 2. y 3. –5, –2 and 2 4. True 5. False 6. True 7. B 8. E 9. H 10. D 11. I 12. A 13. L 14. C 15. F 16. J 17. G 18. K 19. y = ( x - 4) 3 20. y = ( x + 4) 3 21. y = x 3 + 4 22. y = x 3 - 4 23. y = - x ( 29 3 = - x 3 24. y = - x 3 25. y = 4 x 3 26. y = 1 4 x 3 = x 3 64 27. (1) y = x + 2 28. (1) y = - x (2) y = - x + 2 ( 29 (3) y = - - x + 2 ( 29 = - - x - 2 (2) y = - x - 3 (3) y = - x - 3 - 2 29. (1) y = - x 30. (1) y = x + 2 (2) y = - x + 2 (3) y = - x + 3 + 2 (2) y = - x + 2 (3) y = - ( x + 3) + 2 = - x - 3 + 2 31. c 32. d 33. c 34. a
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Chapter 3 Functions and Their Graphs 334 35. f ( x ) = x 2 - 1 Using the graph of y = x 2 , vertically shift downward 1 unit. 36. f ( x ) = x 2 + 4 Using the graph of y = x 2 , vertically shift upward 4 units. 37. g ( x ) = x 3 + 1 Using the graph of y = x 3 , vertically shift upward 1 unit. 38. g ( x ) = x 3 - 1 Using the graph of y = x 3 , vertically shift downward 1 unit. 39. h ( x ) = x - 2 Using the graph of y = x , horizontally shift to the right 2 units. 40. h ( x ) = x + 1 Using the graph of y = x , horizontally shift to the left 1 unit.
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Section 3.5 Graphing Techniques: Transformations 335 41. f ( x ) = ( x - 1) 3 + 2 Using the graph of y = x 3 , horizontally shift to the right 1 unit, then vertically shift up 2 units. 42. f ( x ) = ( x + 2) 3 - 3 Using the graph of y = x 3 , horizontally shift to the left 2 units, then vertically shift down 3 units. 43. g ( x ) = 4 x Using the graph of y = x , vertically stretch by a factor of 4. 44. g ( x ) = 1 2 x Using the graph of y = x , vertically compress by a factor of 1 2 . 45. h ( x ) = 1 2 x = 1 2 1 x Using the graph of y = 1 x , vertically compress by a factor of 1 2 . 46. h ( x ) = 3 x 3 Using the graph of y = x 3 , vertically stretch by a factor of 3.
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Chapter 3 Functions and Their Graphs 336 47. f ( x ) = - x 3 Reflect the graph of y = x 3 , about the x -axis. 48. f ( x ) = - x Reflect the graph of y = x , about the x -axis. 49.
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3_5 - Chapter 3 Functions and Their Graphs 3.5 1. 3. 5. 7....

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