National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Horizontal and Vertical Asymptotes
Dr. Math answers 'why would a line cross a horizontal asymptote?'.
Richland Community College
Richland Community College: Rational Functions and Asymptotes
This site contains basic information on rational functions. Gives definition, how to find domain and roots, and how rational functions apply to asymptotes and holes in the graph.
Texas Instruments
Texas Instruments: Evaluating Rational Functions
In this activity, students study the asymptotic behavior of rational functions. They explore the two types of asymptotes and make generalizations as to when they do or do not occur.
Texas Instruments
Texas Instruments: Rational Functions Asymptotes and Holes
These multiple-choice and fill-in-the-blank questions ask students to identify asymptotes, holes, and domain for rational functions.
Texas Instruments
Texas Instruments: Graphing the Rational Function F(x)=1/x
This is designed for Algebra 2 students to help them develop an understanding of transformations, asymptotes, domain and range.
Texas Instruments
Texas Instruments: Conic Sections
These questions ask students to write the equations of conic sections given a variety of information. Students are also asked to find the foci of an ellipse and the asymptotes of a hyperbola. Solutions and explanations are included.
Texas Instruments
Texas Instruments: Rational Functions and Their Asymptotes
In these questions, students identify asymptotes and removable discontinuities of rational functions, simplify rational expressions, and solve rational equations. Solutions and explanations are included.
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.
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.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Asintotas
In this unit you will learn to calculate the limits of a function and the equations of the vertical, horizontal and oblique asymptotes from its graph.
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
Sierra College: Conics
Provides the locus of points, dominant axis and equation, discriminant, center, vertex, focus, directrix, and asymptotes for the parabola, the ellipse, and the hyperbola.
![Franklin University: Rational Functions and Asymptotes [Pdf] Website](https://d15y2dacu3jp90.cloudfront.net/images/attachment_defaults/resource/large/FPO-knovation.png "Franklin University: Rational Functions and Asymptotes [Pdf] Website")
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...
Free Math Help
Free Math Help: Asymptotes
Learners investigate asymptotes. The resource includes definitions, examples, graphs, and a message board.
CK-12 Foundation
Ck 12: Analysis: Polynomial and Rational Inequalities
[Free Registration/Login may be required to access all resource tools.] In this lesson students explore analytical, graphical and numerical methods of solving polynomial and rational equations.
Sophia Learning
Sophia: Graphing Inverse Variation Functions
This learning tutorial about how to graph inverse variation functions combines videos, a PowerPoint presentation, and helpful hints. The videos demonstrate how to solve example problems and the PowerPoint presentation provides some key...
Sophia Learning
Sophia: Lio + Lola: Graphing Rational Functions
Graph rational functions using examples and step by step guide.
Analyze Math
Analyze Math: Unit Circle and Trigonometric Functions
The free mathematics tutorial explores the unit circle and trigonometric functions. The tutorial consists of definitions and examples with solutions. The interactive applet allows students to investigate domain, range, and asymptotes of...
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...
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...
Purple Math
Purplemath: Slant (Oblique)l Asymptotes
The functions and graphs of functions with oblique asymptotes are explained with a step-by-step description of how to find oblique asymptotes and gives examples.
Purple Math
Purplemath: Vertical Asymptotes
This Purple Math lesson provides an explanation and examples on vertical asymptotes.