Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Procedimiento Para Analizar Una Funcion
Use this unit to learn and practice the general procedure for representing curves in the form y=f(x). It provides a more advanced look at polynomial and rational functions with interactive graphs.
University of Saskatchewan (Canada)
University of Saskatchewan: Easy Rational Function Exercises
Provides a set of basic exercises on rational expressions, complete with solutions and hints for students.
University of Saskatchewan (Canada)
University of Saskatchewan: Moderate Rational Function Problems
A set of exercises of moderate difficulty on rational functions, complete with solutions and hints for students..
University of Saskatchewan (Canada)
University of Saskatchewan: Advanced Rational Function Problems
A set of more difficult exercises on rational functions, complete with solutions. Asks for students to find the asymptotes of the equations given and to sketch the function.
Other
Franklin University: Rational Functions and Asymptotes [Pdf]
This site provides an introduction to rational functions. Topics that are included are finding the domain of a rational function, finding the horizontal and vertical asymptotes and graphing rational functions. There are many worked out...
New York University
Nyu: Courant Institute of Mathematical Sciences: Rational Functions [Pdf]
This site provides a detailed explanation of rational functions by looking at numerous examples. Topics that are covered include domain, horizontal asymptotes, vertical asymptotes and graphing rational functions.
Other
Binghamton University: Graphing Rational Functions [Pdf]
This site is a 16-page excerpt from a textbook that discusses the topic of graphing rational functions. The book includes numerous worked out examples. Topics that are covered include the domain of a rational function, zeroes of a...
PBS
Pbs Teachers: Building Boxes [Pdf]
By determining the dimensions necessary for building a box with the greatest volume, students will explore the world of polynomial and rational expressions. Graphing calculators can be used for this activity.
Paul Dawkins
Paul's Online Notes: Math Notes: Excluded Values in Rational Functions
A description and example of which values are excluded from the domain of a rational function.
Analyze Math
Analyze Math: Rational Expressions
Learners are introduced to the Pre-Calculus topic of rational expressions. The tutorial consists of a definition, examples, and finding the domain of rational expression. The activity includes practice exercises with detailed solutions.
University of Saskatchewan (Canada)
University of Saskatchewan: Graphing Rational Functions
Offers a straightforward introduction to graphing rational functions. Includes an example.
Richland Community College
Richland Community College: Steps to Graphing Rational Functions
This site describes the steps to follow when graphing a rational function.
Science and Mathematics Initiative for Learning Enhancement (SMILE)
Smile: Real World Applications Work Problems
A lesson plan incorporating the use of real world work, rate, and time problems. Examples are provided and strategies for effective use of the lesson are included.
Analyze Math
Analyze Math: Simplify Rational Expressions
Learners explore the Pre-Calculus concept of rational expressions. The tutorial examines how to simplify rational expressions. The activity consists of examples and practice exercises with detailed solutions.
Analyze Math
Analyze Math: Graphs of Rational Functions
Students explore the graph of a rational function given by its formula. The tutorial examines vertical and horizontal asymptotes. The activity consists of examples with solutions.
Lawrence Hall of Science
The Math Page: Topics in Pre Calculus: Rational Functions
Here is a site that clearly and thoroughly explains how to find the roots of polynomials of degree greater than two. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this...
Cool Math
Coolmath: Rational Functions the Whole Thing
Explanation and examples of rational functions.
Cool Math
Coolmath: Rational Functions Increasing and Decreasing Revisited
Explanation, examples, and independent practice of rational functions that increase and decrease.
Cool Math
Coolmath: Review What Are Rational Functions?
One page reference sheet of a quick recall of rational functions.
Cool Math
Coolmath: Graphing Rational Functions X and Y Intercepts
Find out how to find the x and y-intercepts when graphing rational functions.
Cool Math
Coolmath: Graphing Rational Functions Vertical Asymptotes
This Precalculus review (Calculus preview) lesson explains how to find the vertical asymptotes when graphing rational functions.
Cool Math
Coolmath: Graphing Rational Functions Putting It All Together
A tutorial reviewing graphing rational functions.