Answer
1) Domain: $(-\infty,-2.4]$
2) Range: $[0,\infty )$
Work Step by Step
Given \begin{equation}
h(x)=\sqrt{-5 x-12}= \sqrt{-5 \left(x+\frac{12}{5}\right)}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$-5 \left(x+\frac{12}{5}\right)\geq 0\implies x\leq -\frac{12}{5}= -2.4.$$ 1) The domain is $(-\infty,-2.4]$.
2) The range is $[0,\infty )$.
See the graph for proof.
