The rational function $f$ is defined by an equation in the form $f(x)=\frac{a}{x+b}$. The partial graph of $y=f(x)$ is shown. The graph of $f(x)$ has a vertical asymptote at $x=-4$. A new function $h(x)$ is defined as $h(x)=f(x-3)$. What is the equation of the vertical asymptote of $h(x)$?