How do you find the asymptotes for #f(x) = 1 /(x^2-2x-8)#?
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:
Therefore, the above lines will cause asymptotic behaviour as the curve approaches. You can substitute values of x such 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