the graph of h(x) is a translation of f(x) = ∛x. which equation represents h(x)? h(x) = ∛(x - 2) h(x) = ∛(x…

Explanation:

Step1: Recall translation rules

For a function $y = f(x)$, a horizontal translation $a$ units to the right is $y=f(x - a)$ and a vertical translation $b$ units up is $y=f(x)+b$. The parent - function is $f(x)=\sqrt[3]{x}$.

Step2: Identify the translation from the graph

The point $(0,0)$ on $y = \sqrt[3]{x}$ is translated to $(- 2,0)$ on $h(x)$ horizontally and from $(0,0)$ to $(0,2)$ vertically. The graph of $h(x)$ is a translation of $f(x)=\sqrt[3]{x}$ 2 units to the left and 2 units up. For a horizontal translation 2 units to the left of $y = \sqrt[3]{x}$, we replace $x$ with $(x + 2)$ in the function, and for a vertical translation 2 units up, we add 2 to the function. So $h(x)=\sqrt[3]{x + 2}+2$.

Answer:

$h(x)=\sqrt[3]{x + 2}+2$