Answer
Domain: $(-∞, ∞)$
Range: $(-∞, 1]$
Work Step by Step
Function: $f(x)= -abs(x+1)+1$
There are no fractions in this function, so all real numbers are the domain.
The vertex of the graph is at $(-1,1)$.
$f(x)= -abs(x+1)+1$
$f(-1) =-abs(-1+1)+1$
$f(-1) = -abs (0) +1$
$f(-1) = -0+1$
$f(-1) = 1$
Since this is the vertex, we know that all possible $y$ values of the function are either greater than or less than $1$. Since the graph opens down, we know that the vertex is the maximum value for $y$.
