- Multiplicity of zeroes
- Multiplicity of asymptotes
Zeroes are found in the numerator of a rational function.
If there is a factor with a multiplicity of one, then the line will cross the axis at that intercept.
For example:
If there are factors of a rational function that have an even multiplicity, it means that the line will be tangent (only touching it at one point) to the axis.
For example:
If there are factors that have an odd multiplicity, it means that the line lingers and levels off around the intercept, but does cross the axis at that point.
For example:
MULTIPLICITY OF ASYMPTOTES
Asymptotes are found in the denominator of a rational function.
If an asymptote has an odd multiplicty, then the graph will behave oppositely on either side of the asymptote.
For example:
It goes down on the left side of the asymptote and up on the right side.
If an asymptote has even multiplicity, then the graph will behave the same way on either side of the asymptote.
It goes up on both sides of the asymptote.
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