# How do you find the asymptotes for #f(x) = 1 /(x^2-2x-8)#?

##### 1 Answer

See below.

#### Explanation:

In this particular case, only two things cause asymptotic behaviour: if the denominator is zero, or as

Let's study these individually:

If the denominator is zero:

Then

By factorising:

Finding solutions:

Therefore, the above lines will cause asymptotic behaviour as the curve approaches. You can substitute values of x such as

As

As this occurs, only the term which the largest order will matter (order refers to the power or exponent value). We consider both the top and bottom of the fraction of

So the three asymptote said are