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Rational Expressions, Equations and Functions

Topic Review on "Title":

Rational functions: 
Any function which can be written of the form:

where and are polynomials.

 

Domain of a rational function:
Domain of a rational function is the set of points where the function is defined.

Vertical asymptote:
A line of the form such that takes arbitrarily large values near

Horizontal asymptote:
A line of the form such that if tends to infinity, tends to

The sum of rational functions:
.

The product of rational functions:
.

Simple functions
Simple functions are rational functions that cannot be reduced further.

The division of rational functions:
.


Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial describes the concept of rational functions.  These are a type of polynomial functions whose vertical and horizontal asymptotes helped describe the domain of rational functions. It is important to determine the degrees of the two functions that are part of a rational function so asymptotes could be determined.  

This tutorial describes operations on rational functions through the use of examples. Simplification of rational functions is achieved by factoring the numerator function of rational functions and the denominator function of rational functions. Solving polynomial equations involves comparing the degrees and evaluating both functions so simplification can be achieved as much as possible.


Tutorial Features:

Specific Tutorial Features:
• Simplification techniques are used to reduce rational functions.
• Asymptotes are shown in the examples with the use of graphs.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.


"Title" Topic List:
Basic definitions of rational functions
Domain of rational functions
Asymptotes of rational functions
Formula
Operations on rational functions
Simple rational functions
Simplification of rational functions
Polynomial equations
Solving polynomial equations


See all 24 lessons in College Algebra, including concept tutorials, problem drills and cheat sheets:
Teach Yourself College Algebra Visually in 24 Hours

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