Answer
Domain: All real numbers
Range: All real numbers
Work Step by Step
Given
\begin{equation}
f(x)=\sqrt[3]{x-7}.
\end{equation}
The radical has odd index, $n=3$, therefore the domain and range are all real numbers. We have: \begin{equation}
\begin{aligned}
\text { Domain :All real numbers } \\
\text { Range : All real numbers }
\end{aligned}
\end{equation} Make a table of the function, $f(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & -20& -10 & 10 & 20 \\
\hline \boldsymbol{g}(\boldsymbol{x})=\sqrt[3]{\boldsymbol{x-7}} &
-3& -2.6 & 1.4 & 2.4 \\
\hline
\end{array}
\end{equation} See the graph.
