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.
Anne Arundel Community College
Anne Arundel Community College: Math 131: Graphs of Functions
The tutorial examines graphs of functions. Students learn about the graphs of six functions through examples with detailed solutions.
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...
Other
Desmos: Graphing Calculator
Students can enter functions and equations and create a graph of the function.
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...
Mangahigh
Mangahigh: Algebra: Drawing Curves
Mangahigh is a website with math games aimed at twelve to eighteen year olds. On this site students draw graphs of polynomial functions.
CK-12 Foundation
Ck 12: Algebra: Horizontal and Vertical Asymptotes
[Free Registration/Login may be required to access all resource tools.] Identifying and understanding asymptotes of rational functions
CK-12 Foundation
Ck 12: Algebra: Oblique Asymptotes
[Free Registration/Login may be required to access all resource tools.] In this lesson students gain an understanding of oblique asymptotes of rational functions, and how to locate them. Students examine guided notes, review guided...
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.
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.
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.
Richland Community College
Richland Community College: Steps to Graphing Rational Functions
This site describes the steps to follow when graphing a rational function.
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: 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: Asymptotes
This Purple Math lesson provides practice problems for finding various types of aysmptotes. Each problem is worked out and explained.