The rational function $f$ is defined by an equation in the form $f(x)=\frac{a}{x+b}$, where $a$ and $b$ are constants. The partial graph of $y=f(x)$ is shown. If the graph passes through the points $(1,3)$ and $(3,1)$, which equation could define function $g$ if $g(x)=f(x-2)+1$?