How do you find all the asymptotes for function $y=(x^2-4)/(x)$ ?

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Answer 1 · 2015-09-12T15:55:38

The vertical asymptote is $x=0$ and oblique asymptote
$y=x$

A line $x=a$ is a vertical asymptote of a function f(x) if

$lim_(x->a)f(x)=+-oo$

A line $y = b$ is a horizontal asymptote of a function f(x) if

$lim_(x->+-oo)=b$

An oblique asymptote for a function f(x) has the formula

$y=cx+d$

where

$c=lim_(x->oo)f(x)/x$ and $d=lim_(x->oo)(f(x)-cx)$

Hence we have that

$f(x)->+-oo , x->0$

and $c=limf(x)/x=lim(x^2-4)/x^2=1$

$d=lim((x^2-4)/x-x)=0$

Hence $x=0$ and $y=x$

How do you find all the asymptotes for function y=(x^2-4)/(x)y=(x^2-4)/(x)?