What are all horizontal asymptotes of the graph $y=(5+2^x)/(1-2^x)$ ?

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Answer 1 · 2014-09-22T04:09:35

Let us find limits at infinity.

$lim_{x to +infty}{5+2^x}/{1-2^x}$

by dividing the numerator and the denominator by $2^x$ ,

$=lim_{x to +infty}{5/2^x+1}/{1/2^x-1}={0+1}/{0-1}=-1$

and

$lim_{x to -infty}{5+2^x}/{1-2^x}={5+0}/{1-0}=5$

Hence, its horizontal asymptotes are

$y=-1$ and $y=5$

They look like this:
enter image source here

What are all horizontal asymptotes of the graph y=(5+2^x)/(1-2^x)y=(5+2^x)/(1-2^x) ?