What are the asymptotes of $f(x)=-x/((x^2-8)(9x-2)$ ?

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Answer 1 · 2016-11-22T19:53:24

Horizontal asymptote: at $y=0$ because the degree on top is lower than the degree on bottom.

Vertical asymptotes:
$x=2sqrt2$
$x=-2sqrt2$
$x=2/9$

$f(x)=frac{-x}{(x^2-8)(9x-2)}$

Factor completely:
$f(x)=frac{-x}{(x-sqrt8)(x+sqrt8)(9)(x-2/9)}$

$f(x)=frac{-x}{9(x-2sqrt2)(x+2sqrt2)(x-2/9)}$

Vertical asymptotes occur when the denominator is equal to zero.
Vertical Asymptotes:
$x=2sqrt2$
$x=-2sqrt2$
$x=2/9$

What are the asymptotes of f(x)=-x/((x^2-8)(9x-2) f(x)=-x/((x^2-8)(9x-2) ?