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Graphing Rational Functions

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Examples, solutions, videos, worksheets, and activities to help students learn about how to graph rational functions.

What is a Rational Function?
A rational function is of the form
f(x) = p(x)/q(x) where p(x) and q(x) are polynomials and q(x) ≠ 0.

How to graph rational functions?
Graphs of the form
y = (ax + b)/(cx + d)
1. graphs into hyperbolas
2. vertical asymptote occurs at the x value that makes the denominator = 0.
3. horizontal asymptote occurs at the line y = a/c.

The following diagram shows how to graph rational functions of the form y = (ax + b)/(cx + d). Scroll down the page for more examples and solutions on how to graph rational functions.

Graph Rational Functions

Rational Functions and their Graphs
Learn about rational functions and their graphs

Graphing a Rational Function - Example 1 Graphing a Rational Function - Example 2 Graphing a Rational Function - Example 3 Graphing a Rational Function - Example 4 Graphing Rational Functions
A couple of examples on graphing rational functions.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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