Answer
$f(x)=(x+1)^{2}-1$
Work Step by Step
$f(x)=(x+1)^{2}-1$
$g(x)=(x+1)^{2}+1$
$h(x)=(x-1)^{2}+1$
$j(x)=(x-1)^{2}-1$
First, you will notice the graph has the vertex $(-1,1)$. The $1$ inside the parentheses of $j(x)$ moves to the left one unit and the outside number moves down one unit. Therefore, $f(x)=(x+1)^{2}-1$ is the correct answer.