Question

A function
`f(x)=\sqrt[3]{x}` is transformed into the function
`g(x)=-\sqrt[3]{x} -8`.

Name the 2 transformations that occurred and describe the general shape of g(x). When describing the shape, you have the option of including a picture of its graph.

PLEASE HELP!!!!!

Answer 1

a reflection in the x-axis, and a vertical translation of 8 units down.

Explanation:

The given function is

`f(x) = \sqrt[3]{x}`

The transformed function is

`g(x) = - \sqrt[3]{x} - 8`

We can see that the transformation is of the form

`- f(x) - h`

Where h=8 is a downward shift by 8 units.

And the negation tells us that the parent function is reflected in the x-axis