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