the graph of g(x) is a translation of y = ∛x. which equation represents g(x)? o g(x)=∛(x - 4) o g(x)=∛(x +…

Explanation:

Step1: Recall translation rules

For a function $y = f(x)$, a horizontal translation $h$ units to the right is $y=f(x - h)$ and a vertical translation $k$ units up is $y=f(x)+k$, down is $y = f(x)-k$.

Step2: Analyze the graph

The parent - function is $y=\sqrt[3]{x}$. The graph of $g(x)$ is shifted 4 units to the right compared to $y = \sqrt[3]{x}$. Using the horizontal - translation rule, if we shift $y=\sqrt[3]{x}$ to the right by 4 units, the function becomes $g(x)=\sqrt[3]{x - 4}$.

Answer:

$g(x)=\sqrt[3]{x - 4}$