Rational functions

To graph a rational function, first factor both numerator and denominator.
Cancel any common factors to reduce the fraction.
The roots of the reduced denominator give you vertical asymptotes; each one is a vertical line.
The roots of the factors that you cancelled give you holes; plug each one into the reduced expression to get its other coordinate.
The roots of the reduced numerator give you horizontal intercepts; each one is a point on the horizontal axis.
If you perform long division and throw out the remainder, then you get a polynomial; this is the formula for the other asymptote.
Don't forget the vertical intercept, which works the same way as always.

This web page was written in 2011 by Toby Bartels, last edited on 2011 August 4. Toby reserves no legal rights to it.