Answer
Sample answer: $\displaystyle \quad f(x)=\frac{1}{(x-2)^{2}}$
Work Step by Step
The graph approaches $y=0$, the horizontal asymptote, on both sides of the graph.
$f(x)=0+$(rational expression with degree of numerator less than that of the denominator).
The rational expression should have $x-2$ as a factor of the denominator.
$\displaystyle \frac{1}{x-2}$ is not adequate, as $\displaystyle \lim_{x\rightarrow 2^{-}}\frac{1}{x-2}=-\infty$.
If we square the denominator, then both one-sided limits are $+\infty$,
which is what we want.
Thus, such a function could be:$ \displaystyle \quad f(x)=\frac{1}{(x-2)^{2}}$
