Fixed point stability for an iteration

A fixed point $x_{\ast }$ of $x_{n+1}=g(x_n)$ is locally asymptotically stable when $|g\prime (x_{\ast })|<1$.

A cobweb plot alternates vertical moves to the graph $y=g(x)$ and horizontal moves to the diagonal $y=x$, displaying the iterates of $x_{n+1}=g(x_n)$ geometrically.