Answer
Domain: $(-∞, ∞)$
Range: $(-∞, 3]$
Work Step by Step
Function: $f(x)= -abs(x+2)+3$
There are no fractions in this function, so all real numbers are the domain.
The vertex of the graph is at $(-2,3)$.
$f(x)= -abs(x+2)+3$
$f(-2)= -abs(-2+2)+3$
$f(-2)= -abs 0 +3$
$f(-2)= -0 +3$
$f(-2) =3$
Since this is the vertex, we know that all possible $y$ values of the function are either greater than or less than $3$. Since the graph opens down, we know that the vertex is the maximum value for $y$.