Answer
See graph
Work Step by Step
Given \begin{equation}
g(x)=-\sqrt{x-3}.
\end{equation} This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$x-3\geq 0\implies x\geq 3.$$ 1) The domain is $ x\geq 3$.
Make a table of the function, $g(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & 3 & 5& 10 & 15 \\
\hline \boldsymbol{g}(\boldsymbol{x})=-\sqrt{\boldsymbol{x}-\mathbf{3}} & 0 & -1.4 & -2.6 & -3.5 \\
\hline
\end{array}
\end{equation} Plot the points from the table and join them by a smooth curve to graph the function.
