Answer
Domain: $x \geq -7$
Range: $y \leq 0$
Work Step by Step
Given
\begin{equation}
f(x)=-4.5 \sqrt{x+7}.
\end{equation} The radicand of an even radical function must be positive. This requires us to have $x+7\geq 0\implies x\geq -7$. Since the function is negative, we must have $y\leq 0$.
Hence: \begin{equation}
\begin{aligned}
\text { Domain : } & x \geq -7\\
\text { Range : } & y \leq 0
\end{aligned}
\end{equation}
