# What are the asymptotes of y=1/(x−2) and how do you graph the function?

What are the asymptotes of $y=\frac{1}{x-2}$ and how do you graph the function?
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Lorenzo Aguilar
$y=\frac{1}{x-2}$
y is defined for $x\in \left(-\infty ,2\right)\cup \left(2,+\infty \right)$
Consider $\underset{x\to {2}^{+}}{lim}y=+\infty$
And $\underset{x\to {2}^{-}}{lim}y=-\infty$
Hence, y has a vertical asymptote x=2
Now, consider $\underset{x\to \infty }{lim}y=0$
Hence, y has a horizontal asymptote y=0
y is a rectangular hyperbola with the graph below.
graph{1/(x-2) [-10, 10, -5, 5]}