Solutions to Try Its
1. The graphs of f(x)f(x) and g(x)g(x) are shown below. The transformation is a horizontal shift. The function is shifted to the left by 2 units.
2.

a)

b)
3. g(x)=−f(x)g(x)=−f(x)
xx | -2 | 0 | 2 | 4 |
g(x)g(x) | −5 | −10 | −15 | −20 |
h(x)=f(−x)
x | -2 | 0 | 2 | 4 |
h(x) | 15 | 10 | 5 | unknown |
4. even
5.
x | 2 | 4 | 6 | 8 |
g(x) | 9 | 12 | 15 | 0 |
6. g(x)=3x−2
7. g(x)=f(13x) so using the square root function we get g(x)=√13x
8.
9. g(x)=1x−1+1
10. Notice: g(x)=f(−x) looks the same as f(x) .
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 f, substitute (−x) for (x) in f(x). Simplify. If the resulting function is the same as the original function, f(−x)=f(x), then the function is even. If the resulting function is the opposite of the original function, f(−x)=−f(x), 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. g(x)=|x−1|−3
9. g(x)=1(x+4)2+2
11. The graph of f(x+43) is a horizontal shift to the left 43 units of the graph of f.
13. The graph of f(x−4) is a horizontal shift to the right 4 units of the graph of f.
15. The graph of f(x)+8 is a vertical shift up 8 units of the graph of f.
17. The graph of f(x)−7 is a vertical shift down 7 units of the graph of f.
19. The graph of f(x+4)−1 is a horizontal shift to the left 4 units and a vertical shift down 1 unit of the graph of f.
21. decreasing on (−∞,−3) and increasing on (−3,∞)
23. decreasing on (0,∞)
25.
27.
29.
31. g(x)=f(x−1),h(x)=f(x)+1
33. f(x)=|x−3|−2
35. f(x)=√x+3−1
37. f(x)=(x−2)2
39. f(x)=|x+3|−2
41. f(x)=−√x
43. f(x)=−(x+1)2+2
45. f(x)=√−x+1
47. even
49. odd
51. even
53. The graph of g is a vertical reflection (across the x -axis) of the graph of f.
55. The graph of g is a vertical stretch by a factor of 4 of the graph of f.
57. The graph of g is a horizontal compression by a factor of 15 of the graph of f.
59. The graph of g is a horizontal stretch by a factor of 3 of the graph of f.
61. The graph of g is a horizontal reflection across the y -axis and a vertical stretch by a factor of 3 of the graph of f.
63. g(x)=|−4x|
65. g(x)=13(x+2)2−3
67. g(x)=12(x−5)2+1
69. The graph of the function f(x)=x2 is shifted to the left 1 unit, stretched vertically by a factor of 4, and shifted down 5 units.
71. The graph of f(x)=|x| 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 f(x)=x3 is compressed vertically by a factor of 12.
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 f(x)=√x is shifted right 4 units and then reflected across the vertical line x=4.
79.

81.

Candela Citations
- Precalculus. Authored by: Jay Abramson, et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175. License: CC BY: Attribution. License Terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.