How do you find the horizontal asymptote for # g(x) = (3x^2) / (x^2 - 9)#?

1 Answer
Nov 14, 2015

Answer:

Solve for #x^2-9=0#

Explanation:

In order to find the horizontal asymptote of a function, you have to solve it's denominator, while in order to find the vertical asymptote, you'll have to solve #y=a/c#, such that #y=(ax+b)/(cx+d)#. Note, the principles hold true for all degrees of #x#, so you can also use these two formulae if your function has a squared, or cubic, #x#.

To find the horizontal asymptote of #g(x)#, solve the denominator part. Hence, #x^2-9=0#
#x^2=9#
#x^2=3^2#
so, #x=3#

Therefore the horizontal asymptote of #g(x)# is #x=3#, or #x-3=0#.