Graphing Rational Functions

Recall that rational functions of the form $f(x)=\frac{a}{x-h}+k$ can be called simple rational functions. In this form, $x=h$ is the vertical asymptote and $y=k$ is the horizontal asymptote. With this in mind, let's begin by determining the asymptotes of the given function. $$\begin{array}{c}f(x)=\frac{a}{x-h}+k\to f(x)=\frac{\text{-}2}{x-1}+2\end{array}$$ The vertical asymptote is $x=1$ and the horizontal asymptote is $y=2.$ To graph the function, we will first graph these asymptotes on the coordinate plane.

Next, we will make a table of values. To do so, we will consider $x\text{-}$values both to the left and to the right of the vertical asymptote.

Finally, we can plot the points $(x,f(x))$ on the same coordinate plane and connect them with smooth curves.