# 3.9 Practice Question Solutions

## Verbal Question Solutions

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 $\text{}f\text{}$, substitute $\text{}\left(-x\right)\text{}$ for $\text{}\left(x\right)\text{}$ in $\text{}f\left(x\right)\text{}$. Simplify. If the resulting function is the same as the original function, $\text{}f\left(-x\right)=f\left(x\right)\text{}$ then the function is even. If the resulting function is the opposite of the original function, $\text{}f\left(-x\right)=-f\left(x\right)\text{}$, then the original function is odd. If the function is not the same or the opposite, then the function is neither odd nor even.

## Algebraic Question Solutions

7. $g\left(x\right)=|x-1|-3$

9. $g\left(x\right)=\frac{1}{{\left(x+4\right)}^{2}}+2$

11. The graph of $\text{}f\left(x+43\right)\text{}$ is a horizontal shift to the left 43 units of the graph of $\text{}f$.

13. The graph of $\text{}f\left(x-4\right)\text{}$ is a horizontal shift to the right 4 units of the graph of $\text{}f$.

15. The graph of $\text{}f\left(x\right)+8\text{}$ is a vertical shift up 8 units of the graph of $f.$

17. The graph of $\text{}f\left(x\right)-7\text{}$ is a vertical shift down 7 units of the graph of $\text{}f.$

19. The graph of $f\left(x+4\right)-1$ is a horizontal shift to the left 4 units and a vertical shift down 1 unit of the graph of $f$.

21. decreasing on $\text{}\left(-\infty ,-3\right)\text{}$ and increasing on $\text{}\left(-3,\infty \right)$

23. decreasing on $\left(0,\text{}\infty \right)$

25.

27.

29.

## Numeric Question Solutions

31. $g\left(x\right)=f\left(x-1\right),\text{}h\left(x\right)=f\left(x\right)+1$

33. $f\left(x\right)=|x-3|-2$

35. $f\left(x\right)=\sqrt{x+3}-1$

37. $f\left(x\right)={\left(x-2\right)}^{2}$

39. $f\left(x\right)=|x+3|-2$

41. $f\left(x\right)=-\sqrt{x}$

43. $f\left(x\right)=-{\left(x+1\right)}^{2}+2$

45. $f\left(x\right)=\sqrt{-x}+1$

47. even

49. odd

51. even

53. The graph of $\text{}g\text{}$ is a vertical reflection (across the $\text{}x$ -axis) of the graph of $\text{}f$.

55. The graph of $\text{}g\text{}$ is a vertical stretch by a factor of 4 of the graph of $\text{}f.$

57. The graph of $\text{}g\text{}$ is a horizontal compression by a factor of $\text{}\frac{1}{5}\text{}$ of the graph of $\text{}f$.

59. The graph of $\text{}g\text{}$ is a horizontal stretch by a factor of 3 of the graph of $\text{}f$.

61. The graph of $\text{}g\text{}$ is a horizontal reflection across the $\text{}y$ -axis and a vertical stretch by a factor of 3 of the graph of $\text{}f$.

63. $g\left(x\right)=|-4x|$

65. $g\left(x\right)=\frac{1}{3{\left(x+2\right)}^{2}}-3$

67. $g\left(x\right)=\frac{1}{2}{\left(x-5\right)}^{2}+1$

69. The graph of the function $\text{}f\left(x\right)={x}^{2}\text{}$ is shifted to the left 1 unit, stretched vertically by a factor of 4, and shifted down 5 units.

71. The graph of $\text{}f\left(x\right)=|x|\text{}$ 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 $\text{}f\left(x\right)={x}^{3}\text{}$ is compressed vertically by a factor of $\text{}\frac{1}{2}$.

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 $\text{}f\left(x\right)=\sqrt{x}\text{}$ is shifted right 4 units and then reflected across the vertical line $\text{}x=4$.

79.

81.