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Graphing Rational Functions with Holes

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Examples, videos, worksheets, solutions, and activities to help PreCalculus students learn about graphing rational functions with holes.

How do we find a hole in the graph?
A "hole" in a graph of a rational equation will occur when a value of x causes both the numerator and the denominator to equal 0.

Graphing Rational Functions with Holes

A rational function is a quotient of two functions.
The graph of a rational function usually has vertical asymptotes where the denominator equals 0.
However, the graph of a rational function will have a hole when a value of x causes both the numerator and the denominator to equal 0.
This occurs when there is a common factor in the numerator and denominator. We can set the common factor to zero and solve for x to find the hole.

The following diagram shows how to graph rational functions with holes. Scroll down the page for more examples and solutions on graphing rational functions.

Graph Rational Functions with Holes

Graphing rational functions with holes
How to graph a rational function when there is a common factor in the numerator and denominator?



Graphing a Rational Function with a Hole

Holes in Rational Equations

Coordinates of a Hole of a Rational Function

This video shows how to find the coordinates of a hole in the graph of a rational function.

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