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(a)

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The function is $\"\"$ .

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Horizontal shift : $\"\"$ , shift the graph of $\"\"$ a distance $\"\"$ units to the right.

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Therefore, $\"\"$ is the graph of $\"\"$ shifted to a distance of $\"\"$ units to the right.

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Observe the graph.

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The option $\"\"$ shifted $\"\"$ units to the right.

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Option $\"\"$ is the correct choice for the function $\"\"$ .

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(b)

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The function is $\"\"$ .

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Vertical shift : $\"\"$ , shift the graph of $\"\"$ a distance $\"\"$ units upward.

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Therefore, $\"\"$ is the graph of $\"\"$ shift to a distance of $\"\"$ units upward.

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Observe the graph.

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The option $\"\"$ shifted $\"\"$ units upward.

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Option $\"\"$ is the correct choice for the function $\"\"$ .

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(c)

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The function is $\"\"$ .

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Vertical Shrink : $\"\"$ , shrink the graph of $\"\"$ vertically by a factor of $\"\"$ .

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Therefore, $\"\"$ is the graph of $\"\"$ shrink vertically by a factor of $\"\"$ .

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Observe the graph.

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The option $\"\"$ shrinks vertically by a factor of $\"\"$ .

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Option $\"\"$ is the correct choice for the function $\"\"$ .

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(d)

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The function is $\"\"$ .

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First consider the function $\"\"$ .

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Horizontal shift : $\"\"$ , shift the graph of $\"\"$ a distance $\"\"$ units to the left.

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Therefore, $\"\"$ is the graph of $\"\"$ shift to a distance of $\"\"$ to the left.

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Now $\"\"$

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Reflection : $\"\"$ , reflect the graph of $\"\"$ about the $\"\"$ axis.

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Therefore $\"\"$ is the reflection about the about the $\"\"$ axis and shifted to a distance of $\"\"$ units to the left .

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Observe the graph.

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The option $\"\"$ is shifted $\"\"$ units to the left about the $\"\"$ axis.

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Option $\"\"$ is the correct choice for the function $\"\"$ .

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(e)

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The function is $\"\"$ .

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First consider the function $\"\"$ .

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Horizontal shift : $\"\"$ , shift the graph of $\"\"$ a distance $\"\"$ units to the left.

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Therefore $\"\"$ is the graph of $\"\"$ shift to a distance of $\"\"$ to the left.

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Now $\"\"$

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Vertical stretch : $\"\"$ , stretch the graph of $\"\"$ vertically by a factor of $\"\"$ .

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Therefore, $\"\"$ is shifted $\"\"$ units to the left and stretched vertically by a factor of $\"\"$ .

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Observe the graph.

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The option $\"\"$ shifted $\"\"$ units to the left and stretched vertically by a factor of $\"\"$ .

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Option $\"\"$ is the correct choice for the function $\"\"$ .

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(a) 3

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(b) 1

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(c) 4

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(d) 5

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(e) 2.