Answer
See graph
Work Step by Step
Given \begin{equation}
f(x)=-\sqrt{x-6}.
\end{equation}
a) This is an even root function because the index, $n=2$ is even. The radicand must be positive. So, we require $$x-6\geq 0\implies x\geq 6.$$ 1) The domain is $ x\geq 6$.
Make a table of the function, $f(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & 8 & 10 & 15 & 25 \\
\hline \boldsymbol{f}(\boldsymbol{x})=-\sqrt{\boldsymbol{x}-\mathbf{6}} & -1.4 & -2.0 & -3.0 & -4.4 \\
\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.
