Answer
See graph (red).
domain $(-\infty,\infty)$, range $(-\infty,\infty)$.
Work Step by Step
Step 1. To obtain the graph of $h(x)=\sqrt[3] {2x}$ from $y=\sqrt[3] {x}$, compress the curve horizontally by a factor of $\frac{1}{2}$. See graph (red).
Step 2. We can find the domain $(-\infty,\infty)$ and the range $(-\infty,\infty)$.