Graphing Rational Functions

A rational function in the form $y=\frac{a}{x-h}+k$ has a vertical asymptote at $x=h$ and a horizontal asymptote at $y=k.$ With this, let's determine the asymptote of $h(x).$ $$\begin{array}{c}h(x)=\frac{2}{x+3}+1\iff h(x)=\frac{2}{x-(\text{-}3)}+1\end{array}$$ It has a vertical asymptote at $x=\text{-}3$ and a horizontal asymptote at $y=1.$ Therefore, we can match the function with the graph given in the option B.