Answer
See graph
Work Step by Step
Given \begin{equation}
g(x)=-\sqrt{x+9}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$x+9\geq 0\implies x\geq -9.$$ 1) The domain is $ x\geq -9$.
Make a table of the function $g(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & -5 & 0 & 5 & 15 \\
\hline \boldsymbol{g}(\boldsymbol{x})=-\sqrt{\boldsymbol{x}+\mathbf{9}} & -2.0 & -3.0 & -3.7 & -4.9 \\
\hline
\end{array}
\end{equation} Plot the points from the table and join them by a smooth curve to get the graph of the function.
