- 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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