# Chapter 8, Section 1

Copyright 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 1 Chapter 8 Rational Expressions and Functions Copyright 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 2

8.1 Rational Expressions and Functions; Multiplying and Dividing Copyright 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 3 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. Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 4

8.1 Rational Expressions and Functions; Multiplying and Dividing 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: Copyright 2010 Pearson Education, Inc. All rights reserved.

Sec 8.1 - 5 8.1 Rational Expressions and Functions; Multiplying and Dividing 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. Copyright 2010 Pearson Education, Inc. All rights reserved.

Sec 8.1 - 6 8.1 Rational Expressions and Functions; Multiplying and Dividing Define Rational Functions and Describe Their Domain 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.

Copyright 2010 Pearson Education, Inc. All rights reserved. 2 3 Sec 8.1 - 7 8.1 Rational Expressions and Functions; Multiplying and Dividing Finding Numbers Not in the Domain of a Rational Function

To locate the values not in the domain of a rational function, we need only determine which real numbers make the denominator 0. 3 Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 8 8.1 Rational Expressions and Functions; Multiplying and Dividing

Writing Rational Expressions in Lowest Terms 3 Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 9 8.1 Rational Expressions and Functions; Multiplying and Dividing Writing Rational Expressions in Lowest Terms

3 Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 10 8.1 Rational Expressions and Functions; Multiplying and Dividing When the Numerator and Denominator are Opposites 3

Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 11 8.1 Rational Expressions and Functions; Multiplying and Dividing Multiplying Rational Expressions 3 Copyright 2010 Pearson Education, Inc. All rights reserved.

Sec 8.1 - 12 8.1 Rational Expressions and Functions; Multiplying and Dividing Multiplying Rational Expressions 3 Copyright 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 13

8.1 Rational Expressions and Functions; Multiplying and Dividing Finding the Reciprocal of a Rational Expression 3 Copyright 2010 Pearson Education, Inc. All rights reserved. To find the reciprocal, simply interchange the numerator and

denominator. Sec 8.1 - 14 8.1 Rational Expressions and Functions; Multiplying and Dividing Dividing Rational Expressions 3 Copyright 2010 Pearson Education, Inc. All rights reserved.

Sec 8.1 - 15

## Recently Viewed Presentations

• What went well? What needed to be done differently? ... Survey done 6 months after intervention in one clinic. High satisfaction. 78% rated 8 or above. Interestingly, 42% said they noted a difference while 57 % had not noted a...
• By controlling the length and the branching, you can control the final hardness or flexibility of the polymer plus qualities like resistance to solvents, acids, or heat. The favorite properties of plastics are that they are inert and won't react...
• [email protected] Global Burden of NCDs. NCDs such as cardiovascular, diabetes, cancer, renal, genetic and respiratory conditions are major health threat accounting for : 60%. of deaths . 47%.
• A breach is the acquisition, access, use or disclosure of PHI that is: Not for treatment, payment or healthcare operations. ... Cache is the storage of data that makes future requests for the same data more efficient. Contact IT Support...
• How is a Private Equity Firm Structured? Private Equity Firm (General Partner) Limited Partners (Investors) (public pension funds, corporate pension funds, insurance companies, high net-worth individuals, family offices, endowments, foundations, fund-of-funds, sovereign wealth funds, etc.) Private Equity Fund (Limited Partnership)...
• And he called to the man clothed with linen, which had the writer's inkhorn by his side; * 4 And the Lord said unto him, Go through the midst of the city, through the midst of Jerusalem, and set a...
• * Not shown at Dortmund in winte term 03/04. * Not shown at Dortmund in winte term 03/04. * Not shown at Dortmund in winte term 03/04. * * * * * * Power and Thermal Management Dynamic Voltage Scaling...
• Authority. denotes rule, control, influence, weight, permission, privilege, and power to act when someone has authority . they have charge of others with responsibility beyond the norm. exousia (ex-oo-see'-ah)