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

Answer:

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

Step-by-step 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 $g(x) = \sqrt[3]{-x+5}$