Describing Transformations of Rational Functions

Note that the given rational function is written in the form $g(x)=\frac{1}{b(x-h)}+k.$ Let's identify the transformations that the values of $b,$ $h,$ and $k$ produce.

Let's now identify the constants in the given function rule. $$\begin{array}{c}g(x)=\frac{1}{2(x-3)}+1\iff g(x)=\frac{1}{2(x-3)}+1\end{array}$$ We can see that $b$ $=$ $\frac{1}{2},$ $h$ $=$ $3,$ and $k$ $=$ $1.$ Therefore, the transformations of the parent function that result in the graph of the given function are a horizontal shrunk by a factor of $\frac{1}{2},$ followed by a translation $3$ units right and $1$ unit up. These correspond to choices B, E, and G.