Question

what is the child function of the parent f(x) =/root 3 x if it was translated 5 spaces to the right and reflected about the x axis

Answer 1

The child function is
`g(x) = \sqrt[3]{-x+5}`

Explanation:

Parent function:

In this question, the parent function is
`f(x) = \sqrt[3]{x}`

Translated 5 spaces to the right:

Translating a function 5 units to the right is finding f(x - 5).

In this question:

`f(x-5) = \sqrt[3]{x-5}`

Reflecting a function about the x-axis:

Reflecting a function f(x) about the x-axis is finding f(-x). So

`f(-(x-5)) = \sqrt[3]{-(x-5)}`

`f(-x+5) = \sqrt[3]{-x+5}`

The child function is
`g(x) = \sqrt[3]{-x+5}`