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Question

Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. 14f(x3)+5\frac{1}{4} f(x-3)+5

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Graph of 14f(x3)+5\dfrac{1}{4}f(x-3)+5 can be obtained from f(x)f(x) by three combined translations.

f(x)f(x3)f(x) \rightarrow f(x-3) is shifting 3 units to the right

f(x3)14f(x3)f(x-3)\rightarrow \dfrac{1}{4}f(x-3) is vertical shrink by a factor of 14\dfrac{1}{4}

14f(x3)14f(x3)+5\dfrac{1}{4}f(x-3)\rightarrow \dfrac{1}{4}f(x-3)+5 is shifting 5 units upward

So, graph of 14f(x3)+5\dfrac{1}{4}f(x-3)+5 can be obtained from f(x)f(x) by shifting 3 units to the right, followed by vertical shrink by a factor of 14\dfrac{1}{4} and shifting 5 units up.

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