Answer
Domain: $x\leq 10$
Range: $y \leq 0$
Work Step by Step
Given \begin{equation}
f(x)=-\sqrt{10-x}.
\end{equation} The radicand of an even radical function must be positive. This requires us to have $10-x\geq 0\implies x\leq 10$. Since the function is negative, we must have $y\leq 0$.
Hence: \begin{equation}
\begin{aligned}
\text { Domain : } & x\leq 10\\
\text { Range : } & y \leq 0.
\end{aligned}
\end{equation} Make a table of the function, $f(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & 10& -10 & -60 & -90 \\
\hline \boldsymbol{g}(\boldsymbol{x})=-\sqrt{\boldsymbol{10-x}} & 0 & -4.5 & -8.4 & -10.0 \\
\hline
\end{array}
\end{equation} See the graph.
