Answer
See graph
Work Step by Step
Given \begin{equation}
f(x)=\sqrt{9-x}= \sqrt{-(x-9)}.
\end{equation} This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$-(x-9)\geq 0\implies x-9\leq 0\implies x\leq 9.$$ 1) The domain is $ x\leq 9$.
Make a table of the function, $f(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & -5 & 0 & 3 & 5 \\
\hline \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{9}-\mathbf{x}} & 3.7 & 3 & 2.4 & 2 \\
\hline
\end{array}
\end{equation} Plot the points from the table and join them by a smooth curve to graph the function.
