Answer
See graph
Work Step by Step
Given \begin{equation}
f(x)=-\sqrt{x+3}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$x+3\geq 0\implies x\geq -3.$$ 1) The domain is $[-3, \infty)$.
Make a table of the function, $f(x)$ versus $x$.
\begin{equation}
\begin{array}{|c|cccc|}
\hline \boldsymbol{x} & 2 & 5 & 10 & 15 \\
\hline \boldsymbol{f}(\boldsymbol{x})=-\sqrt{\boldsymbol{x}+\mathbf{3}} & -2.24 & -2.83 & -3.61 & -4.24 \\
\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.
