Question

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

Answer 1

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.