Solutions
Solutions to Try Its
1. The graphs of and are shown below. The transformation is a horizontal shift. The function is shifted to the left by 2 units. 2. a)
b)
3.
-2 | 0 | 2 | 4 | |
-2 | 0 | 2 | 4 | |
15 | 10 | 5 | unknown |
2 | 4 | 6 | 8 | |
9 | 12 | 15 | 0 |
Solution to Odd-Numbered Exercises
1. A horizontal shift results when a constant is added to or subtracted from the input. A vertical shifts results when a constant is added to or subtracted from the output. 3. A horizontal compression results when a constant greater than 1 is multiplied by the input. A vertical compression results when a constant between 0 and 1 is multiplied by the output. 5. For a function , substitute for in . Simplify. If the resulting function is the same as the original function, , then the function is even. If the resulting function is the opposite of the original function, , then the original function is odd. If the function is not the same or the opposite, then the function is neither odd nor even. 7. 9. 11. The graph of is a horizontal shift to the left 43 units of the graph of . 13. The graph of is a horizontal shift to the right 4 units of the graph of . 15. The graph of is a vertical shift up 8 units of the graph of . 17. The graph of is a vertical shift down 7 units of the graph of . 19. The graph of is a horizontal shift to the left 4 units and a vertical shift down 1 unit of the graph of . 21. decreasing on and increasing on 23. decreasing on 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. even 49. odd 51. even 53. The graph of is a vertical reflection (across the -axis) of the graph of . 55. The graph of is a vertical stretch by a factor of 4 of the graph of . 57. The graph of is a horizontal compression by a factor of of the graph of . 59. The graph of is a horizontal stretch by a factor of 3 of the graph of . 61. The graph of is a horizontal reflection across the -axis and a vertical stretch by a factor of 3 of the graph of . 63. 65. 67. 69. The graph of the function is shifted to the left 1 unit, stretched vertically by a factor of 4, and shifted down 5 units. 71. The graph of is stretched vertically by a factor of 2, shifted horizontally 4 units to the right, reflected across the horizontal axis, and then shifted vertically 3 units up. 73. The graph of the function is compressed vertically by a factor of . 75. The graph of the function is stretched horizontally by a factor of 3 and then shifted vertically downward by 3 units. 77. The graph of is shifted right 4 units and then reflected across the vertical line . 79.
81.