Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Asintotas
This interactive unit shows you the relationship between functions and their graphs. You can practice how to calculate the limit of the function as x approaches plus or minus infinity.
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..
Other
Mr. Perez Online Math Tutor: Solving Rational Equations
The mathematics tutorial investigates how to simplify rational equations, find the least common denominator as well as how to solve rational equations. There are notes, examples and an interactive applet as well as a vocabulary puzzle.
Northeast Parallel Architectures Center, Syracuse University
Npac Reu Program: Infinite Limits
This Northeast Parallel Architectures Center at Syracuse University site provides a brief description and examples of infinite limits of functions at infinity.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Graphing Rational Functions
Fourteen problems present a variety of practice graphing rational functions. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the "View Solution" button to...
University of Saskatchewan (Canada)
University of Saskatchewan: Graphing Rational Functions
Offers a straightforward introduction to graphing rational functions. Includes an example.
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.
Khan Academy
Khan Academy: Rational Function Points of Discontinuity
Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive...
Purple Math
Purplemath: Vertical Asymptotes
This Purple Math lesson provides an explanation and examples on vertical asymptotes.
Paul Dawkins
Paul's Online Notes: Infinite Limits: Practice Page
Review exercise provides eight problems that provide practice in evaluating infinite limits and vertical asymptotes.
Illustrative Mathematics
Illustrative Mathematics: F Bf,if the Canoe Trip, Variation 2
In this task about canoeing, paddling speed, and current speed, students examine how long a trip would take at different speeds. They write a function equation, graph their equation, and explain their thinking. The primary purpose of the...
Purple Math
Purplemath: Graphing Rational Functions: Introduction
To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph. Once you get the swing of things, rational functions are actually fairly simple to graph. This resources provides...
CK-12 Foundation
Ck 12: Algebra: Graphs of Rational Functions
[Free Registration/Login may be required to access all resource tools.] Learn about the shapes and characteristics of graphs of rational functions. Students examine guided notes, review guided practice, watch instructional videos and...
CK-12 Foundation
Ck 12: Algebra: Horizontal and Vertical Asymptotes
[Free Registration/Login may be required to access all resource tools.] Find the horizontal and vertical asymptotes of rational functions.
Cool Math
Coolmath: Rational Functions Horizontal Asymptotes (And Slants)
This CoolMath resource provides information about horizontal asymptotes, a type of rational function.
Math Open Reference
Math Open Reference: A Formal View of Limits
Explore the triangle inequality theorem with this helpful reference tool. Provides a detailed definition and an interactive activity that enhances further explanation. Includes links to related topics.
