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Introduction to Rational Functions

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

The following diagram shows the rules for the vertical asymptotes and horizontal asymptotes for rational functions. Scroll down the page for more examples and solutions on graphing rational functions using the asymptotes.

Rational Function Asymptotes

Introduction to Rational Functions
Once we have a thorough understanding of polynomials we can look at rational functions that are a quotient of two polynomials. These rational functions have certain behaviors, and students are often asked to find their limits, or to graph them. Their graphs can have different characteristics depending on whether the numerator function has degree less than, equal to, or greater than the denominator function.

How to define rational functions, and how to identify their domain and zeros?

An introduction to rational functions, including discussion of vertical and horizontal asymptotes
Introduction to Rational Expressions
Finding the Excluded Domain Values of a Rational Function, Recognizing and finding Asymptotes, and Graphing Rational Functions using Asymptotes.

Try the free Mathway calculator and problem solver below to practice various 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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