## Finding Equations of Asymptotes

The easiest asymptotes to find are those which result from the factorisation of the denominator.

If then there are asymptotes at An asymptote that results from the highest power of in the numerator being one larger than the highest power of in the denominator or vice versa is also easily found. - find the equations of the asymptotes.

We divide top and bottom by and take the limit as The equation of one asymptote is and the equation of the other is since the denominator has a root at  – find the equations of the asymptotes.

we divide top and bottom by and take the limit as The equation of one asymptote is and the equation of the other is since the denominator has a root at If the power of in the denominator is higher than the power of in the numerator than there is always an asymptote at  - find the equations of the asymptotes.

We divide top and bottom by and take the limit as The equation of one asymptote is and the equation of the other is since the denominator has a root at If the highest powers of in numerator and denominator are the same then there is an asymptote at the quotient of these coefficients. 