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 $(2,-4)$ and $(4,-2)$, which equation could define function $g$ if $g(x)=-f(x+1)$?