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What are the effects on the graph of when it is transformed to

What are the effects on the graph of when it is transformed to-example-1
User Arlg
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Recall the following two function transformations:

Vertical stretch by a factor k:


f\lparen x)\rightarrow k\cdot f\lparen x)

Horizontal translation by c units:


f\lparen x)=f\lparen x-c)

Notice that starting with the parent function f(x):


f\lparen x)=\sqrt[3]{x}

We can apply a vertical stretch by a factor of 4 and a horizontal translation by 7 units left to get h(x):


\sqrt[3]{x}\rightarrow4\sqrt[3]{x}\rightarrow4\sqrt[3]{x-\left(-7\right)}=4\sqrt[3]{x+7}

Therefore, the effects when f(x) is transformed to h(x) are:

- A vertical stretch by a factor of 4.

- A horizontal translation 7 units left.

User JVC
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