Question

How do I write the given description in box 2 onto box 4, using the the transformational formula on box 1?

Answer 1

We have

$g(x)=a\sqrt[3]{b(x-h)}+k$

Reflection over y-axis and Horizontal compression by a factor of 2 --- b=-2

vertical shift down 1 --- k=-1

there is no horizontal shift, therefore h=0

there is no vertical stretch, therefore a=1

the function is

$g(x)=1\sqrt[3]{-2(x-0)}-1$$g(x)=\sqrt[3]{-2x}-1$