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3.5E: Transformation of Functions (Exercises)

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    56073
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    For the following exercises, sketch a graph of the given function.

    45. \(f(x)=(x-3)^{2}\)
    46. \(f(x)=(x+4)^{3}\)
    47. \(f(x)=\sqrt{x}+5\)
    48. \(f(x)=-x^{3}\)
    49. \(f(x)=\sqrt[3]{-x}\)
    50. \(f(x)=5 \sqrt{-x}-4\)
    51. \(f(x)=4[|x-2|-6]\)
    52. \(f(x)=-(x+2)^{2}-1\)

    For the following exercises, sketch the graph of the function \(g\) if the graph of the function \(f\) is shown Figure \(\PageIndex{1}\).

    Graph of f(x)
    Figure \(\PageIndex{1}\)

    53. \(g(x)=f(x-1)\)
    54. \(g(x)=3 f(x)\)

    For the following exercises, write the equation for the standard function represented by each of the graphs below.

    55.

    Graph of an absolute function.

    56.

    Graph of a half circle.

    For the following exercises, determine whether each function below is even, odd, or neither.

    57. \(f(x)=3 x^{4}\)
    58. \(g(x)=\sqrt{x}\)
    59. \(h(x)=\frac{1}{x}+3 x\)

    For the following exercises, analyze the graph and determine whether the graphed function is even, odd, or neither.

    60.

    Graph of a parabola.

    61.

    Graph of a parabola.

    62.

    Graph of a cubic function.


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