Answer
1) Domain: $(-\infty,3]$
2) Range: $[0,\infty )$.
Work Step by Step
Given \begin{equation}
h(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 $$-x+3\geq 0\implies x\leq 3.$$ 1)The domain is $(-\infty,3]$
2) The range is $[0,\infty )$.
See the graph for proof.
