How+to+find+asymptotes

Greetings,
You have come here to discover how to unlock the calculations of finding asymptotes.

You have come to the right place.

To find asymptotes, you must make sure that the function is rational, that is: It is in the form N(x) / D(x)

these can be any form of polynomial, but make sure they are in standard form and simplified, this will be needed later.

Once you have the function properly written, we need to decide which type of asymptote we are looking for.

If we are looking for vertical, we have a simple job:

find the zeroes of D(x), that is find where the function can not exist due to dividing by zero!

If we are looking for the horizontal asymptotes we have three possibilites.

In all of these options, we will be looking at the degree of equation.


 * NOTE: the degree of an equation is the highest power of the polynomial, for example a second degree equation has x 2 + 2x + 10.

IF: the degree of the numerator is smaller then that of the denominator, then the horizontal asymptote will be at y = 0. Think about it, if the denominator grows faster than the numerator, that function will constantly get closer to zero.

IF: the degrees of the numerator and denominator are equal, the the asymptote will be on the ratio of the two leading coefficients. For example, if the function if (3x 2 - 42) / ( 2x 2 ), then the asymptote will be on y = 3/2.

IF: the degree of the numerator is bigger then that of the denominator, there isn't a horizontal asymptote. Think about it, if the function keeps increasing, at an increasing rate, will it stop?

THERE YOU GO! HOW TO FIND ASYMPTOTES!
GO LEARN, I KNOW YOU CAN!