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Edition: 3RD 07

Copyright: 2007

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Copyright: 2007

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

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Algebra: A Combined Approach is intended for a 2-semester sequence of Introductory and Intermediate Algebra where students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course.

**Chapter R Prealgebra Review **

R.1 Factors and the Least Common Multiple

R.2 Fractions

R.3 Decimals and Percents

**Chapter 1. Real Numbers and Introduction to Algebra **

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Exponents, Order of Operations, and Variable Expressions

1.4 Adding Real Numbers

1.5 Subtracting Real Numbers

Integrated Review-Operations on Real Numbers

1.6 Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

**Chapter 2. Equations, Inequalities, and Problem Solving **

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Further Solving Linear Equations

Integrated Review-Solving Linear Equations

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Solving Linear Inequalities

**Chapter 3. Graphing Equations and Inequalities **

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

Integrated Review-Summary of Linear Equations

3.5 Equations of Lines

3.6 Graphing Linear Inequalities in Two Variables

**Chapter 4. Systems of Equations **

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

Integrated Review-Summary on Solving Systems of Equations

4.4 Systems of Linear Equations and Problem Solving

**Chapter 5. Exponents and Polynomials **

5.1 Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products

Integrated Review-Exponents and Operations on Polynomials

5.7 Dividing Polynomials

**Chapter 6. Factoring Polynomials **

6.1 The Greatest Common Factor

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c

6.4 Factoring Trinomials of the Form ax² + bx + c by Grouping

6.5 Factoring Special Products

Integrated Review-Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

**Chapter 7. Rational Expressions **

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least

Common Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Solving Equations Containing Rational Expressions

Integrated Review-Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Expressions

7.7 Simplifying Complex Fractions

**Chapter 8. Graphs and Functions **

8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines

8.2 Introduction to Functions

8.3 Polynomial and Rational Functions

Integrated Review-Linear Equations in Two Variables

8.4 Interval Notation, Finding Domains and Ranges from Graphs and Graphing Piecewise Defined Functions

8.5 Shifting and Reflecting Graphs of Functions

**Chapter 9. Systems of Equations and Inequalities, and Variation **

9.1 Solving Systems of Linear Equations and Problem Solving in Three Variables

9.2 Solving Systems of Equations Using Matrices

Integrated Review-Systems of Linear Equations

9.3 Systems of Linear Inequalities

9.4 Variation and Problem Solving

**Chapter 10. Rational Exponents, Radicals and Complex Numbers **

10.1 Radical Expressions and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Numerators and Denominators of Radical Expressions

Integrated Review-Radicals and Rational Exponents

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

**Chapter 11. Quadratic Equations and Functions**

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by Using the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods

Integrated Review-Summary on Solving Quadratic Equations

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

**Chapter 12. Exponential and Logarithmic Functions **

12.1 The Algebra of Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Logarithmic Functions

12.5 Properties of Logarithms

Integrated Review-Functions and Properties of Logarithms

12.6 Common Logarithms, Natural Logarithms, and Change of Base

12.7 Exponential and Logarithmic Equations and Problem Solving

**Chapter 13. Conic Sections **

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

Integrated Review-Graphing Conic Sections

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and systems of Inequalities

**Appendices **

A Transition Review: Exponents, Polynomials and Factoring Strategies

B Transition Review: Solving Linear and Quadratic Equations

C The Bigger Picture-Simplifying Expressions and Solving Equations

D Sets and Compound Inequalities

E Absolute Value Equations and Inequalities

F Determinants and Cramer's Rule

G Review of Angles, Lines and Special Triangles

H An Introduction to Using a Graphing Utility

I. Stretching Graphs of Absolute Value Functions

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Summary

Algebra: A Combined Approach is intended for a 2-semester sequence of Introductory and Intermediate Algebra where students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course.

Table of Contents

**Chapter R Prealgebra Review **

R.1 Factors and the Least Common Multiple

R.2 Fractions

R.3 Decimals and Percents

**Chapter 1. Real Numbers and Introduction to Algebra **

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Exponents, Order of Operations, and Variable Expressions

1.4 Adding Real Numbers

1.5 Subtracting Real Numbers

Integrated Review-Operations on Real Numbers

1.6 Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

**Chapter 2. Equations, Inequalities, and Problem Solving **

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Further Solving Linear Equations

Integrated Review-Solving Linear Equations

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Solving Linear Inequalities

**Chapter 3. Graphing Equations and Inequalities **

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

Integrated Review-Summary of Linear Equations

3.5 Equations of Lines

3.6 Graphing Linear Inequalities in Two Variables

**Chapter 4. Systems of Equations **

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

Integrated Review-Summary on Solving Systems of Equations

4.4 Systems of Linear Equations and Problem Solving

**Chapter 5. Exponents and Polynomials **

5.1 Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products

Integrated Review-Exponents and Operations on Polynomials

5.7 Dividing Polynomials

**Chapter 6. Factoring Polynomials **

6.1 The Greatest Common Factor

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c

6.4 Factoring Trinomials of the Form ax² + bx + c by Grouping

6.5 Factoring Special Products

Integrated Review-Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

**Chapter 7. Rational Expressions **

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least

Common Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Solving Equations Containing Rational Expressions

Integrated Review-Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Expressions

7.7 Simplifying Complex Fractions

**Chapter 8. Graphs and Functions **

8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines

8.2 Introduction to Functions

8.3 Polynomial and Rational Functions

Integrated Review-Linear Equations in Two Variables

8.4 Interval Notation, Finding Domains and Ranges from Graphs and Graphing Piecewise Defined Functions

8.5 Shifting and Reflecting Graphs of Functions

**Chapter 9. Systems of Equations and Inequalities, and Variation **

9.1 Solving Systems of Linear Equations and Problem Solving in Three Variables

9.2 Solving Systems of Equations Using Matrices

Integrated Review-Systems of Linear Equations

9.3 Systems of Linear Inequalities

9.4 Variation and Problem Solving

**Chapter 10. Rational Exponents, Radicals and Complex Numbers **

10.1 Radical Expressions and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Numerators and Denominators of Radical Expressions

Integrated Review-Radicals and Rational Exponents

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

**Chapter 11. Quadratic Equations and Functions**

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by Using the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods

Integrated Review-Summary on Solving Quadratic Equations

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

**Chapter 12. Exponential and Logarithmic Functions **

12.1 The Algebra of Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Logarithmic Functions

12.5 Properties of Logarithms

Integrated Review-Functions and Properties of Logarithms

12.6 Common Logarithms, Natural Logarithms, and Change of Base

12.7 Exponential and Logarithmic Equations and Problem Solving

**Chapter 13. Conic Sections **

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

Integrated Review-Graphing Conic Sections

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and systems of Inequalities

**Appendices **

A Transition Review: Exponents, Polynomials and Factoring Strategies

B Transition Review: Solving Linear and Quadratic Equations

C The Bigger Picture-Simplifying Expressions and Solving Equations

D Sets and Compound Inequalities

E Absolute Value Equations and Inequalities

F Determinants and Cramer's Rule

G Review of Angles, Lines and Special Triangles

H An Introduction to Using a Graphing Utility

I. Stretching Graphs of Absolute Value Functions

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Published: 2007

International: No

**Chapter R Prealgebra Review **

R.1 Factors and the Least Common Multiple

R.2 Fractions

R.3 Decimals and Percents

**Chapter 1. Real Numbers and Introduction to Algebra **

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Exponents, Order of Operations, and Variable Expressions

1.4 Adding Real Numbers

1.5 Subtracting Real Numbers

Integrated Review-Operations on Real Numbers

1.6 Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

**Chapter 2. Equations, Inequalities, and Problem Solving **

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Further Solving Linear Equations

Integrated Review-Solving Linear Equations

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Solving Linear Inequalities

**Chapter 3. Graphing Equations and Inequalities **

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

Integrated Review-Summary of Linear Equations

3.5 Equations of Lines

3.6 Graphing Linear Inequalities in Two Variables

**Chapter 4. Systems of Equations **

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

Integrated Review-Summary on Solving Systems of Equations

4.4 Systems of Linear Equations and Problem Solving

**Chapter 5. Exponents and Polynomials **

5.1 Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products

Integrated Review-Exponents and Operations on Polynomials

5.7 Dividing Polynomials

**Chapter 6. Factoring Polynomials **

6.1 The Greatest Common Factor

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c

6.4 Factoring Trinomials of the Form ax² + bx + c by Grouping

6.5 Factoring Special Products

Integrated Review-Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

**Chapter 7. Rational Expressions **

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least

Common Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Solving Equations Containing Rational Expressions

Integrated Review-Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Expressions

7.7 Simplifying Complex Fractions

**Chapter 8. Graphs and Functions **

8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines

8.2 Introduction to Functions

8.3 Polynomial and Rational Functions

Integrated Review-Linear Equations in Two Variables

8.4 Interval Notation, Finding Domains and Ranges from Graphs and Graphing Piecewise Defined Functions

8.5 Shifting and Reflecting Graphs of Functions

**Chapter 9. Systems of Equations and Inequalities, and Variation **

9.1 Solving Systems of Linear Equations and Problem Solving in Three Variables

9.2 Solving Systems of Equations Using Matrices

Integrated Review-Systems of Linear Equations

9.3 Systems of Linear Inequalities

9.4 Variation and Problem Solving

**Chapter 10. Rational Exponents, Radicals and Complex Numbers **

10.1 Radical Expressions and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Numerators and Denominators of Radical Expressions

Integrated Review-Radicals and Rational Exponents

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

**Chapter 11. Quadratic Equations and Functions**

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by Using the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods

Integrated Review-Summary on Solving Quadratic Equations

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

**Chapter 12. Exponential and Logarithmic Functions **

12.1 The Algebra of Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Logarithmic Functions

12.5 Properties of Logarithms

Integrated Review-Functions and Properties of Logarithms

12.6 Common Logarithms, Natural Logarithms, and Change of Base

12.7 Exponential and Logarithmic Equations and Problem Solving

**Chapter 13. Conic Sections **

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

Integrated Review-Graphing Conic Sections

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and systems of Inequalities

**Appendices **

A Transition Review: Exponents, Polynomials and Factoring Strategies

B Transition Review: Solving Linear and Quadratic Equations

C The Bigger Picture-Simplifying Expressions and Solving Equations

D Sets and Compound Inequalities

E Absolute Value Equations and Inequalities

F Determinants and Cramer's Rule

G Review of Angles, Lines and Special Triangles

H An Introduction to Using a Graphing Utility

I. Stretching Graphs of Absolute Value Functions