- 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.

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

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