Question

A function LaTeX: f\left(x\right)=\sqrt[3]{x}f ( x ) = x 3 is transformed into the function LaTeX: g\left(x\right)=-\sqrt[3]{x}-8g ( x ) = − x 3 − 8. Name the 2 transformations that occurred and describe the general shape of g(x).

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`

To see the transformation that occurred, we can rewrite g(x) in terms of f(x).

That is:

`g(x) = - f(x) - 8`

Therefore f(x) is reflected in the x-axis and translated 8 units down.

The resulting graph decreases from left to right over its entire domain.