copyright © 2010 pearson education, inc. all rights reserved sec 8.1 - 1


Rational Expressions and Functions

Chapter 8


8.1

Rational Expressions and Functions;

Multiplying and Dividing

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 4

8.1 Rational Expressions and Functions; Multiplying and Dividing

Objectives

1. Define rational expressions.

2. Define rational functions and describe their domains.

3. Write rational expressions in lowest terms.

4. Multiply rational expressions.

5. Find reciprocals for rational expressions.

6. Divide rational expressions.



Defining Rational Expressions

In Section 1.1, we defined rational numbers to be the quotient of two integers, a / b with b not equal to 0.

A rational expression (algebraic fraction) is the quotient of two polynomials, also with the denominator not 0. Rational expressions are the elements of the set

Examples:



Define Rational Functions and Describe Their Domain

A rational function has the form

The domain of a rational function includes all the real numbers except those that make Q(x), the denominator, equal to 0.



Define Rational Functions and Describe Their Domain

33

2

The graph of the function f(x) is shown at the right. The domain of this function is all real numbers except x = 3 where f(x) is not defined.



Finding Numbers Not in the Domain of a Rational Function

3

To locate the values not in the domain of a rational function, we need only determine which real numbers make the denominator 0.



Writing Rational Expressions in Lowest Terms

3



When the Numerator and Denominator are Opposites

3



Multiplying Rational Expressions

3



Finding the Reciprocal of a Rational Expression

3To find the reciprocal, simply interchange the numerator and denominator.



Dividing Rational Expressions

3

copyright © 2010 pearson education, inc. all rights reserved sec 8.1 - 1

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