Answer
The graph is a circle with a center at $(-1,0)$ and a radius of $r=1.$ See details below.
Work Step by Step
$\begin{align*}
\vert z+1\vert &= 1 \\
\vert (x+iy)+1\vert &= 1 \\
\vert (x+1) +iy\vert &= 1 \\
\sqrt{(x+1)^2 + y^2} &= 1 \\
(x+1)^2 + y^2 &= 1
\end{align*}$
The graph is a circle with a center at $(-1,0)$ and a radius of $r=1$.
