{"id":975,"date":"2015-11-12T18:37:58","date_gmt":"2015-11-12T18:37:58","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=975"},"modified":"2017-03-31T21:04:26","modified_gmt":"2017-03-31T21:04:26","slug":"section-exercises-57","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/section-exercises-57\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"
\r\n
\r\n\r\n1. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?\r\n\r\n2. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?\r\n\r\n3. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?\r\n\r\n4. When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?\r\n\r\n5. How can you determine whether a function is odd or even from the formula of the function?\r\n\r\n6.\u00a0Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\sqrt{x}[\/latex] is shifted up 1 unit and to the left 2 units.\r\n\r\n7. Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=|x|[\/latex]\r\nis shifted down 3 units and to the right 1 unit.\r\n\r\n8.\u00a0Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\frac{1}{x}[\/latex] is shifted down 4 units and to the right 3 units.\r\n\r\n9. Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex] is shifted up 2 units and to the left 4 units.\r\n\r\nFor the following exercises, describe how the graph of the function is a transformation of the graph of the original function [latex]f[\/latex].\r\n\r\n10. [latex]y=f\\left(x - 49\\right)[\/latex]\r\n\r\n11. [latex]y=f\\left(x+43\\right)[\/latex]\r\n\r\n12.\u00a0[latex]y=f\\left(x+3\\right)[\/latex]\r\n\r\n13. [latex]y=f\\left(x - 4\\right)[\/latex]\r\n\r\n14.\u00a0[latex]y=f\\left(x\\right)+5[\/latex]\r\n\r\n15. [latex]y=f\\left(x\\right)+8[\/latex]\r\n\r\n16.\u00a0[latex]y=f\\left(x\\right)-2[\/latex]\r\n\r\n17. [latex]y=f\\left(x\\right)-7[\/latex]\r\n\r\n18.\u00a0[latex]y=f\\left(x - 2\\right)+3[\/latex]\r\n\r\n19. [latex]y=f\\left(x+4\\right)-1[\/latex]\r\n\r\nFor the following exercises, determine the interval(s) on which the function is increasing and decreasing.\r\n\r\n20. [latex]f\\left(x\\right)=4{\\left(x+1\\right)}^{2}-5[\/latex]\r\n\r\n21. [latex]g\\left(x\\right)=5{\\left(x+3\\right)}^{2}-2[\/latex]\r\n\r\n22.\u00a0[latex]a\\left(x\\right)=\\sqrt{-x+4}[\/latex]\r\n\r\n23. [latex]k\\left(x\\right)=-3\\sqrt{x}-1[\/latex]\r\n\r\nFor the following exercises, use the graph of [latex]f\\left(x\\right)={2}^{x}[\/latex]\u00a0to sketch a graph of each transformation of [latex]f\\left(x\\right)[\/latex].\r\n\"Graph\r\n\r\n24. [latex]g\\left(x\\right)={2}^{x}+1[\/latex]\r\n\r\n25. [latex]h\\left(x\\right)={2}^{x}-3[\/latex]\r\n\r\n26. [latex]w\\left(x\\right)={2}^{x - 1}[\/latex]\r\n\r\nFor the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.\r\n\r\n27. [latex]f\\left(t\\right)={\\left(t+1\\right)}^{2}-3[\/latex]\r\n\r\n28.\u00a0[latex]h\\left(x\\right)=|x - 1|+4[\/latex]\r\n\r\n29. [latex]k\\left(x\\right)={\\left(x - 2\\right)}^{3}-1[\/latex]\r\n\r\n30.\u00a0[latex]m\\left(t\\right)=3+\\sqrt{t+2}[\/latex]\r\n\r\n31.\u00a0Tabular representations for the functions [latex]f,g[\/latex], and [latex]h[\/latex] are given below. Write [latex]g\\left(x\\right)[\/latex] and [latex]h\\left(x\\right)[\/latex] as transformations of [latex]f\\left(x\\right)[\/latex].\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr>
[latex]f\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n\u22123<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr><\/tbody><\/table>
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\r\n
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\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n2<\/td>\r\n3<\/td>\r\n<\/tr>
[latex]g\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n\u22123<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr><\/tbody><\/table>
[latex]x[\/latex]<\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr>
[latex]h\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n\u22122<\/td>\r\n2<\/td>\r\n3<\/td>\r\n<\/tr><\/tbody><\/table><\/div>\r\n
\r\n

32.\u00a0Tabular representations for the functions [latex]f,g[\/latex], and [latex]h[\/latex] are given below. Write [latex]g\\left(x\\right)[\/latex] and [latex]h\\left(x\\right)[\/latex] as transformations of [latex]f\\left(x\\right)[\/latex].<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr>
[latex]f\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22121<\/td>\r\n\u22123<\/td>\r\n4<\/td>\r\n2<\/td>\r\n1<\/td>\r\n<\/tr><\/tbody><\/table>
[latex]x[\/latex]<\/strong><\/td>\r\n\u22123<\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n<\/tr>
[latex]g\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22121<\/td>\r\n\u22123<\/td>\r\n4<\/td>\r\n2<\/td>\r\n1<\/td>\r\n<\/tr><\/tbody><\/table>
[latex]x[\/latex]<\/strong><\/td>\r\n\u22122<\/td>\r\n\u22121<\/td>\r\n0<\/td>\r\n1<\/td>\r\n2<\/td>\r\n<\/tr>
[latex]h\\left(x\\right)[\/latex] <\/strong><\/td>\r\n\u22122<\/td>\r\n\u22124<\/td>\r\n3<\/td>\r\n1<\/td>\r\n0<\/td>\r\n<\/tr><\/tbody><\/table><\/div>\r\n<\/div>\r\n

For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions.<\/p>\r\n\r\n

\r\n
\r\n\r\n33.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

34.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n35.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

36.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n37.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

38.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n39.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

40.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.<\/p>\r\n\r\n

\r\n
\r\n\r\n41.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

42.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n

For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.<\/p>\r\n\r\n

\r\n
\r\n\r\n43.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

44.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n45.\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n
\r\n

46.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n\r\n\"Graph<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, determine whether the function is odd, even, or neither.<\/p>\r\n\r\n

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\r\n

47. [latex]f\\left(x\\right)=3{x}^{4}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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48.\u00a0[latex]g\\left(x\\right)=\\sqrt{x}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

49. [latex]h\\left(x\\right)=\\frac{1}{x}+3x[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

50. [latex]f\\left(x\\right)={\\left(x - 2\\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

51. [latex]g\\left(x\\right)=2{x}^{4}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

52.\u00a0[latex]h\\left(x\\right)=2x-{x}^{3}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function [latex]f[\/latex].<\/p>\r\n\r\n

\r\n
\r\n

53. [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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54.\u00a0[latex]g\\left(x\\right)=f\\left(-x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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\r\n

55. [latex]g\\left(x\\right)=4f\\left(x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

56.\u00a0[latex]g\\left(x\\right)=6f\\left(x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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\r\n

57. [latex]g\\left(x\\right)=f\\left(5x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

58.\u00a0[latex]g\\left(x\\right)=f\\left(2x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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\r\n

59. [latex]g\\left(x\\right)=f\\left(\\frac{1}{3}x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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60.\u00a0[latex]g\\left(x\\right)=f\\left(\\frac{1}{5}x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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\r\n

61. [latex]g\\left(x\\right)=3f\\left(-x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

62.\u00a0[latex]g\\left(x\\right)=-f\\left(3x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, write a formula for the function [latex]g[\/latex] that results when the graph of a given toolkit function is transformed as described.<\/p>\r\n\r\n

\r\n
\r\n

63. The graph of [latex]f\\left(x\\right)=|x|[\/latex] is reflected over the [latex]y[\/latex] -<\/em>axis and horizontally compressed by a factor of [latex]\\frac{1}{4}[\/latex]\u00a0.<\/p>\r\n64.\u00a0The graph of [latex]f\\left(x\\right)=\\sqrt{x}[\/latex] is reflected over the [latex]x[\/latex] -axis and horizontally stretched by a factor of 2.\r\n

\r\n
\r\n

65. The graph of [latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex] is vertically compressed by a factor of [latex]\\frac{1}{3}[\/latex], then shifted to the left 2 units and down 3 units.<\/p>\r\n\r\n<\/div>\r\n

\r\n

66.\u00a0The graph of [latex]f\\left(x\\right)=\\frac{1}{x}[\/latex] is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

67. The graph of [latex]f\\left(x\\right)={x}^{2}[\/latex] is vertically compressed by a factor of [latex]\\frac{1}{2}[\/latex], then shifted to the right 5 units and up 1 unit.<\/p>\r\n\r\n<\/div>\r\n

\r\n

68. The graph of [latex]f\\left(x\\right)={x}^{2}[\/latex] is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.<\/p>\r\n\r\n

\r\n
\r\n

69. [latex]g\\left(x\\right)=4{\\left(x+1\\right)}^{2}-5[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n
\r\n
\r\n

70. [latex]g\\left(x\\right)=5{\\left(x+3\\right)}^{2}-2[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

71. [latex]h\\left(x\\right)=-2|x - 4|+3[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n
\r\n
\r\n

72. [latex]k\\left(x\\right)=-3\\sqrt{x}-1[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

73. [latex]m\\left(x\\right)=\\frac{1}{2}{x}^{3}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n
\r\n
\r\n

74. [latex]n\\left(x\\right)=\\frac{1}{3}|x - 2|[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

75. [latex]p\\left(x\\right)={\\left(\\frac{1}{3}x\\right)}^{3}-3[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

76.\u00a0[latex]q\\left(x\\right)={\\left(\\frac{1}{4}x\\right)}^{3}+1[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

77. [latex]a\\left(x\\right)=\\sqrt{-x+4}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n

For the following exercises, use the graph below\u00a0to sketch the given transformations.\r\n\"Graph<\/span><\/p>\r\n\r\n

\r\n
\r\n

78. [latex]g\\left(x\\right)=f\\left(x\\right)-2[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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79. [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n
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80. [latex]g\\left(x\\right)=f\\left(x+1\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

81. [latex]g\\left(x\\right)=f\\left(x - 2\\right)[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

1. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?<\/p>\n

2. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?<\/p>\n

3. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?<\/p>\n

4. When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?<\/p>\n

5. How can you determine whether a function is odd or even from the formula of the function?<\/p>\n

6.\u00a0Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\sqrt{x}[\/latex] is shifted up 1 unit and to the left 2 units.<\/p>\n

7. Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=|x|[\/latex]
\nis shifted down 3 units and to the right 1 unit.<\/p>\n

8.\u00a0Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\frac{1}{x}[\/latex] is shifted down 4 units and to the right 3 units.<\/p>\n

9. Write a formula for the function obtained when the graph of [latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex] is shifted up 2 units and to the left 4 units.<\/p>\n

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function [latex]f[\/latex].<\/p>\n

10. [latex]y=f\\left(x - 49\\right)[\/latex]<\/p>\n

11. [latex]y=f\\left(x+43\\right)[\/latex]<\/p>\n

12.\u00a0[latex]y=f\\left(x+3\\right)[\/latex]<\/p>\n

13. [latex]y=f\\left(x - 4\\right)[\/latex]<\/p>\n

14.\u00a0[latex]y=f\\left(x\\right)+5[\/latex]<\/p>\n

15. [latex]y=f\\left(x\\right)+8[\/latex]<\/p>\n

16.\u00a0[latex]y=f\\left(x\\right)-2[\/latex]<\/p>\n

17. [latex]y=f\\left(x\\right)-7[\/latex]<\/p>\n

18.\u00a0[latex]y=f\\left(x - 2\\right)+3[\/latex]<\/p>\n

19. [latex]y=f\\left(x+4\\right)-1[\/latex]<\/p>\n

For the following exercises, determine the interval(s) on which the function is increasing and decreasing.<\/p>\n

20. [latex]f\\left(x\\right)=4{\\left(x+1\\right)}^{2}-5[\/latex]<\/p>\n

21. [latex]g\\left(x\\right)=5{\\left(x+3\\right)}^{2}-2[\/latex]<\/p>\n

22.\u00a0[latex]a\\left(x\\right)=\\sqrt{-x+4}[\/latex]<\/p>\n

23. [latex]k\\left(x\\right)=-3\\sqrt{x}-1[\/latex]<\/p>\n

For the following exercises, use the graph of [latex]f\\left(x\\right)={2}^{x}[\/latex]\u00a0to sketch a graph of each transformation of [latex]f\\left(x\\right)[\/latex].
\n\"Graph<\/p>\n

24. [latex]g\\left(x\\right)={2}^{x}+1[\/latex]<\/p>\n

25. [latex]h\\left(x\\right)={2}^{x}-3[\/latex]<\/p>\n

26. [latex]w\\left(x\\right)={2}^{x - 1}[\/latex]<\/p>\n

For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.<\/p>\n

27. [latex]f\\left(t\\right)={\\left(t+1\\right)}^{2}-3[\/latex]<\/p>\n

28.\u00a0[latex]h\\left(x\\right)=|x - 1|+4[\/latex]<\/p>\n

29. [latex]k\\left(x\\right)={\\left(x - 2\\right)}^{3}-1[\/latex]<\/p>\n

30.\u00a0[latex]m\\left(t\\right)=3+\\sqrt{t+2}[\/latex]<\/p>\n

31.\u00a0Tabular representations for the functions [latex]f,g[\/latex], and [latex]h[\/latex] are given below. Write [latex]g\\left(x\\right)[\/latex] and [latex]h\\left(x\\right)[\/latex] as transformations of [latex]f\\left(x\\right)[\/latex].<\/p>\n\n\n\n\n
[latex]x[\/latex]<\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n
[latex]f\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n\u22123<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
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[latex]x[\/latex]<\/strong><\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n<\/tr>\n
[latex]g\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n\u22123<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
[latex]x[\/latex]<\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n
[latex]h\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22121<\/td>\n0<\/td>\n\u22122<\/td>\n2<\/td>\n3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
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32.\u00a0Tabular representations for the functions [latex]f,g[\/latex], and [latex]h[\/latex] are given below. Write [latex]g\\left(x\\right)[\/latex] and [latex]h\\left(x\\right)[\/latex] as transformations of [latex]f\\left(x\\right)[\/latex].<\/p>\n<\/div>\n<\/div>\n

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[latex]x[\/latex]<\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n
[latex]f\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22121<\/td>\n\u22123<\/td>\n4<\/td>\n2<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
[latex]x[\/latex]<\/strong><\/td>\n\u22123<\/td>\n\u22122<\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n<\/tr>\n
[latex]g\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22121<\/td>\n\u22123<\/td>\n4<\/td>\n2<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
[latex]x[\/latex]<\/strong><\/td>\n\u22122<\/td>\n\u22121<\/td>\n0<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n
[latex]h\\left(x\\right)[\/latex] <\/strong><\/td>\n\u22122<\/td>\n\u22124<\/td>\n3<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions.<\/p>\n

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33.
\n\"Graph<\/span><\/p>\n<\/div>\n

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34.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n

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35.
\n\"Graph<\/span><\/p>\n<\/div>\n

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36.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n

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37.
\n\"Graph<\/span><\/p>\n<\/div>\n

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38.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n

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39.
\n\"Graph<\/span><\/p>\n<\/div>\n

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40.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n

For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.<\/p>\n

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41.
\n\"Graph<\/span><\/p>\n<\/div>\n

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42.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/div>\n<\/div>\n

For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.<\/p>\n

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43.
\n\"Graph<\/span><\/p>\n<\/div>\n

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44.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n

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45.
\n\"Graph<\/span><\/p>\n<\/div>\n

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46.<\/p>\n<\/div>\n<\/div>\n

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\"Graph<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following exercises, determine whether the function is odd, even, or neither.<\/p>\n

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47. [latex]f\\left(x\\right)=3{x}^{4}[\/latex]<\/p>\n<\/div>\n

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48.\u00a0[latex]g\\left(x\\right)=\\sqrt{x}[\/latex]<\/p>\n<\/div>\n<\/div>\n

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49. [latex]h\\left(x\\right)=\\frac{1}{x}+3x[\/latex]<\/p>\n<\/div>\n<\/div>\n

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50. [latex]f\\left(x\\right)={\\left(x - 2\\right)}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n

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51. [latex]g\\left(x\\right)=2{x}^{4}[\/latex]<\/p>\n<\/div>\n

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52.\u00a0[latex]h\\left(x\\right)=2x-{x}^{3}[\/latex]<\/p>\n<\/div>\n<\/div>\n

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function [latex]f[\/latex].<\/p>\n

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53. [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex]<\/p>\n<\/div>\n

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54.\u00a0[latex]g\\left(x\\right)=f\\left(-x\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

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55. [latex]g\\left(x\\right)=4f\\left(x\\right)[\/latex]<\/p>\n<\/div>\n

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56.\u00a0[latex]g\\left(x\\right)=6f\\left(x\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

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57. [latex]g\\left(x\\right)=f\\left(5x\\right)[\/latex]<\/p>\n<\/div>\n

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58.\u00a0[latex]g\\left(x\\right)=f\\left(2x\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

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59. [latex]g\\left(x\\right)=f\\left(\\frac{1}{3}x\\right)[\/latex]<\/p>\n<\/div>\n

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60.\u00a0[latex]g\\left(x\\right)=f\\left(\\frac{1}{5}x\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

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61. [latex]g\\left(x\\right)=3f\\left(-x\\right)[\/latex]<\/p>\n<\/div>\n

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62.\u00a0[latex]g\\left(x\\right)=-f\\left(3x\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

For the following exercises, write a formula for the function [latex]g[\/latex] that results when the graph of a given toolkit function is transformed as described.<\/p>\n

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63. The graph of [latex]f\\left(x\\right)=|x|[\/latex] is reflected over the [latex]y[\/latex] –<\/em>axis and horizontally compressed by a factor of [latex]\\frac{1}{4}[\/latex]\u00a0.<\/p>\n

64.\u00a0The graph of [latex]f\\left(x\\right)=\\sqrt{x}[\/latex] is reflected over the [latex]x[\/latex] -axis and horizontally stretched by a factor of 2.<\/p>\n

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65. The graph of [latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex] is vertically compressed by a factor of [latex]\\frac{1}{3}[\/latex], then shifted to the left 2 units and down 3 units.<\/p>\n<\/div>\n

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66.\u00a0The graph of [latex]f\\left(x\\right)=\\frac{1}{x}[\/latex] is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.<\/p>\n<\/div>\n<\/div>\n

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67. The graph of [latex]f\\left(x\\right)={x}^{2}[\/latex] is vertically compressed by a factor of [latex]\\frac{1}{2}[\/latex], then shifted to the right 5 units and up 1 unit.<\/p>\n<\/div>\n

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68. The graph of [latex]f\\left(x\\right)={x}^{2}[\/latex] is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.<\/p>\n<\/div>\n<\/div>\n

For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.<\/p>\n

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69. [latex]g\\left(x\\right)=4{\\left(x+1\\right)}^{2}-5[\/latex]<\/p>\n<\/div>\n

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70. [latex]g\\left(x\\right)=5{\\left(x+3\\right)}^{2}-2[\/latex]<\/p>\n<\/div>\n<\/div>\n

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71. [latex]h\\left(x\\right)=-2|x - 4|+3[\/latex]<\/p>\n<\/div>\n

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72. [latex]k\\left(x\\right)=-3\\sqrt{x}-1[\/latex]<\/p>\n<\/div>\n<\/div>\n

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73. [latex]m\\left(x\\right)=\\frac{1}{2}{x}^{3}[\/latex]<\/p>\n<\/div>\n

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74. [latex]n\\left(x\\right)=\\frac{1}{3}|x - 2|[\/latex]<\/p>\n<\/div>\n<\/div>\n

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75. [latex]p\\left(x\\right)={\\left(\\frac{1}{3}x\\right)}^{3}-3[\/latex]<\/p>\n<\/div>\n

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76.\u00a0[latex]q\\left(x\\right)={\\left(\\frac{1}{4}x\\right)}^{3}+1[\/latex]<\/p>\n<\/div>\n<\/div>\n

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77. [latex]a\\left(x\\right)=\\sqrt{-x+4}[\/latex]<\/p>\n<\/div>\n

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For the following exercises, use the graph below\u00a0to sketch the given transformations.
\n\"Graph<\/span><\/p>\n

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78. [latex]g\\left(x\\right)=f\\left(x\\right)-2[\/latex]<\/p>\n<\/div>\n<\/div>\n

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79. [latex]g\\left(x\\right)=-f\\left(x\\right)[\/latex]<\/p>\n<\/div>\n

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80. [latex]g\\left(x\\right)=f\\left(x+1\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n

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81. [latex]g\\left(x\\right)=f\\left(x - 2\\right)[\/latex]<\/p>\n<\/div>\n

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Candela Citations<\/h3>\n\t\t\t\t\t
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