Texas Education Agency
Texas Gateway: Rational Functions: Predicting the Effects of Parameter Changes
Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.
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.
![Nyu: Courant Institute of Mathematical Sciences: Rational Functions [Pdf] Unknown Type](https://d15y2dacu3jp90.cloudfront.net/images/attachment_defaults/resource/large/FPO-knovation.png "Nyu: Courant Institute of Mathematical Sciences: Rational Functions [Pdf] Unknown Type")
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
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
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...
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) = |X|
This LearningCheck document can be used as a self-discovery lesson. The student can explore the domain and range along with the transformations.
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.
Math Medics
S.o.s. Math: Algebra
This lesson provides basic instruction on the major concepts in algebra. Content includes a focus on fractions, units of conversion, complex numbers, quadratic equations, factorization and roots of polynomials, solving equations, systems...
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.
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.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Domain and Range
This page from the Math Forum contains a question and answer session on how to find range in rational functions. Example problem is given.
Khan Academy
Khan Academy: Intro to Rational Expressions
This lesson will introduce you to rational expressions. You will learn how to determine when a rational expression is undefined and how to find its domain.
Texas A&M University
Wtamu Virtual Math Lab: Intermediate Algebra
This site is a tutorial for students in algebra 2 or for those who need a refresher. The site has explanations, definitions, examples, practice problems and practice tests are found covering topics such as linear equations, graphing,...