How to find the asymptotes of #f(x) =(9x^2 – 36)/( x^2 - 9)# ?

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Answer 1 · 2016-01-11T00:38:20

Vertical asymptotes occur when the denominator equals #0# ...

Vertical Asymptotes :
#x^2-9=0#
#x^2=9#
#x=3 " or " x=-3#

Horizontal Asymptotes :
Find the highest exponents in the numerator and denominator, then divide ...

#y=(9x^2)/x^2=9#

So, #y=9# is the horizontal asymptote.

Here is a graph. The dotted lines are the asymptotes ...

Hope that helped

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