Horizontal Asymptotes

Question : To find the vertical asymptotes of the rational functions is far easy than to find the horizontal asymptotes.

Answer :

The following are some useful tips to find the horizontal asymptotes.

Horizontal asymptotes are horizontal lines the graph approaches.

Horizontal Asymptotes CAN be crossed.

To find horizontal asymptotes:

* If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
* If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
* If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

One way to remember this is the following pneumatic device: BOBO BOTN EATS DC

* BOBO - Bigger on bottom, y=0
* BOTN - Bigger on top, none
* EATS DC - Exponents are the same, divide coefficients