# How do you find all the asymptotes for function y=2/(x-1)+ 1?

Jan 16, 2016

#### Answer:

First you make the denominator go to zero, later you make $x$ go to infinity.

#### Explanation:

The first happens when $x$ goes down to 1 and $y$ will get larger and larger, or in the language:
${\lim}_{x \to 1 +} y = \infty$
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We also have $x$ going up to 1 and $y$ will be larger but negative:
${\lim}_{x \to 1 -} y = - \infty$

The second happens when $x$ goes very large, either positive or negative. The first part will the go to $0$ $y$ will go to $1$
${\lim}_{x \to \pm \infty} y = 1$

Answer: $x = 1 \mathmr{and} y = 1$
graph{2/(x-1)+1 [-20.27, 20.26, -10.14, 10.13]}