Question

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

Answer 1

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`.