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More About This Textbook
Overview
The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer’s personality shows in his writing, as he draws readers into the material through relevant and thoughtprovoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!
Editorial Reviews
From The Critics
This textbook for a onesemester course in intermediate algebra covers functions, systems of linear equations, polynomial factoring, rational expressions, radical exponents, quadratic equations, logarithms, conic sections, sequences, and series. The second edition has been rewritten to make it more accessible, and adds a separate chapter on inequalities. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Meet the Author
Read an Excerpt
Intermediate Algebra for College Students, Third Edition, provides comprehensive, indepth coverage of the topics required in a oneterm course in intermediate algebra. The book is written for college students who have had a course in introductory algebra. The primary goals of the Third Edition are to help students acquire a solid foundation in intermediate algebra and to show how algebra can model and solve authentic realworld problems.
Writing the Third Edition
A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:
I thought about both of these objections in writing every page of the Third Edition.
"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in the Third Edition have been extensively rewritten to make them more accessible. I have paid close attention to ensuring that the amount of detail and depth of coverage is appropriate for an intermediate college algebra course. Every section has been rewritten to contain a better range of simple, intermediate, and challenging examples. Voice balloons allow for more specific annotations in examples, further clarifying procedures and concepts. A more open format gives the book a less crowded look than the Second Edition.
"The applications are not interesting." One of the things I enjoy most about teaching in a large urban community collegeis the diversity of who my students are and what interests them. Realworld data that celebrate this variety are used to bring relevance to examples, discussions, and applications. Most data from the previous edition have been replaced to include data that extend as far up to the present as possible. Updated realworld data were selected on the basis of being interesting and intriguing to students. By connecting algebra to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.
New to the Third Edition
The Third Edition is a significant revision of the Second Edition, with increased emphasis on the relevance of algebra in everyday aspects of students' lives. In addition to the book's new open look, the expanded explanations, and the updated realworld data, you will find the following new features in the Third Edition.
Preserved and Expanded from the Second Edition. The features described below that helped make the Second Edition so popular continue in the Third Edition.
Supplements for the instructor
Printed Resources
Annotated Instructor's Edition (0130614521)
Answers to exercises on the same text page or in Graphing Answer Section.
Graphing Answer Section contains answers to exercises requiring graphical solutions.
Instructor's Solutions Manual (0130342912)
Stepbystep solutions for every evennumbered section exercise.
Stepbystep solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.
Instructor's Resource Manual (0130342807)
Notes to the Instructor
Eight Chapter Tests per chapter (5 free response, 3 multiple choice)
Eight Final Exams ( 4 free response, 4 multiple choice)
Twenty additional exercises per section for added test exercises or worksheets.
Answers to all items
Media Resources
TestGenEQ with QuizMasterEQ (CD ROM for IBM and Macintosh 0130619361)
Algorithmically driven, text specific testing program.
Networkable for administering tests and capturing grades online.
Edit or add your own questions to create a nearly unlimited number of tests and worksheets.
Use the new "Function Plotter" to create graphs.
Tests can be easily exported to HTML so they can be posted to the Web.
Computerized Tutorial Software Course Management System
MathPro Explorer 4.0
Network version for IBM and Macintosh
Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.
Includes an email function for networked users, enabling instructors to send a message to a specific student or to an entire group.
Network based reports and summaries for a class or student and for cumulative or selected scores are available.
MathPro 5
Anytime. Anywhere.
Online tutorial with enhanced class and student management features.
Integration of TestGenEQ allows for testing to operate within the tutorial environment.
Course management tracking of both tutorial and testing activity.
Online Options for Distance Learning
WebCT/Blackboard/CourseCompass
Prentice Hall offers three different online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.
Supplements for the Student
Printed Resources
Student Solutions Manual (0130342890)
Stepbystep solutions for every oddnumbered section exercise.
Stepbystep solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.
How to Study Mathematics
Have your instructor contact the local Prentice Hall sales representative.
Math on the Internet: A Student's Guide
Have your instructor contact the local Prentice Hall sales representative.
Media Resources
Computerized Tutorial Software
MathPro Explorer 4.0
Keyed to each section of the text for textspecific tutorial exercises and instruction.
Warmup exercises and graded Practice Problems.
Video clips show a problem being explained and worked out on the board.
Algorithmically generated exercises. Online help, glossary and summary of scores.
MathPro 5Anytime. Anywhere.
Enhanced, Internetbased version of Prentice Hall's popular tutorial software.
Lecture Videos
Keyed to each section of the text.
Digitized Lecture Videos on CD.
Have your instructor contact the local Prentice Hall sales representative.
Prentice Hall Tutor Center
Provides oneonone tutorial assistance by phone, email, or fax.
Companion Website
Offers Warmups, Real World Activities and Chapter Quizzes.
Email results to your instructor.
Destination links provide additional opportunities to explore other related sites.
To The Student
I've written this book so that you can learn about the power of algebra and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and workedout examples that present solutions in a stepbystep manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra to your life to make your learning experience both interesting and relevant.
As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:
1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed.
2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These workedout examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific workedout examples.
3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.
4. Prepare for chapter exams. After completing a chapter, study the summary chart, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book.
5. Use the supplements available with this book. A solutions manual containing workedout solutions to the book's oddnumbered exercises, all review exercises, and all Check Points, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.
I wrote this book in Point Reyes National Seashore, 40 miles north of San Francisco. The park consists of 75,000 acres with miles of pristine surfwashed beaches, forested ridges, and bays bordered by white cliffs. It was my hope to convey the beauty and excitement of mathematics using nature's unspoiled beauty as a source of inspiration and creativity. Enjoy the pages that follow as you empower yourself with the algebra needed to succeed in college, your career, and in your life.
Regards,
Bob
Robert Blitzer
Table of Contents
1. Algebra, Mathematical Models, and Problem Solving
1.1 Algebraic Expressions, Real Numbers, and Interval Notation
1.2 Operations with Real Numbers and Simplifying Algebraic Expressions
1.3 Graphing Equations
1.4 Solving Linear Equations
MidChapter Check Point Section 1.1–Section 1.4
1.5 Problem Solving and Using Formulas
1.6 Properties of Integral Exponents
1.7 Scientific Notation
Chapter 1 Group Project
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
2. Functions and Linear Functions
2.1 Introduction to Functions
2.2 Graphs of Functions
2.3 The Algebra of Functions
MidChapter Check Point Section 2.1–Section 2.3
2.4 Linear Functions and Slope
2.5 The PointSlope Form of the Equation of a Line
Chapter 2 Group Project
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises (Chapters 1–2)
3. Systems of Linear Equations
3.1 Systems of Linear Equations in Two Variables
3.2 Problem Solving and Business Applications Using Systems of Equations
3.3 Systems of Linear Equations in Three Variables
MidChapter Check Point Section 3.1–Section 3.3
3.4 Matrix Solutions to Linear Systems
3.5 Determinants and Cramer's Rule
Chapter 3 Group Project
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises (Chapters 1–3)
4. Inequalities and Problem Solving
4.1 Solving Linear Inequalities
4.2 Compound Inequalities
4.3 Equations and Inequalities Involving Absolute Value
MidChapter Check Point Section 4.1–Section 4.3
4.4 Linear Inequalities in Two Variables
4.5 Linear Programming
Chapter 4 Group Project
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Exercises (Chapters 1–4)
5. Polynomials, Polynomial Functions, and Factoring
5.1 Introduction to Polynomials and Polynomial Functions
5.2 Multiplication of Polynomials
5.3 Greatest Common Factors and Factoring By Grouping
5.4 Factoring Trinomials
MidChapter Check Point Section 5.1–Section 5.4
5.5 Factoring Special Forms
5.6 A General Factoring Strategy
5.7 Polynomial Equations and Their Applications
Chapter 5 Group Project
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises (Chapters 1–5)
6. Rational Expressions, Functions, and Equations
6.1 Rational Expressions and Functions: Multiplying and Dividing
6.2 Adding and Subtracting Rational Expressions
6.3 Complex Rational Expressions
6.4 Division of Polynomials
MidChapter Check Point Section 6.1–Section 6.4
6.5 Synthetic Division and the Remainder Theorem
6.6 Rational Equations
6.7 Formulas and Applications of Rational Equations
6.8 Modeling Using Variation
Chapter 6 Group Project
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises (Chapters 1–6)
7. Radicals, Radical Functions, and Rational Exponents
7.1 Radical Expressions and Functions
7.2 Rational Exponents
7.3 Multiplying and Simplifying Radical Expressions
7.4 Adding, Subtracting, and Dividing Radical Expressions
MidChapter Check Point Section 7.1–Section 7.4
7.5 Multiplying with More Than One Term and Rationalizing Denominators
7.6 Radical Equations
7.7 Complex Numbers
Chapter 7 Group Project
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
8. Quadratic Equations and Functions
8.1 The Square Root Property and Completing the Square
8.2 The Quadratic Formula
8.3 Quadratic Functions and Their Graphs
MidChapter Check Point Section 8.1–Section 8.3
8.4 Equations Quadratic in Form
8.5 Polynomial and Rational Inequalities
Chapter 8 Group Project
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
9. Exponential and Logarithmic Functions
9.1 Exponential Functions
9.2 Composite and Inverse Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithms
MidChapter Check Point Section 9.1–Section 9.4
9.5 Exponential and Logarithmic Equations
9.6 Exponential Growth and Decay; Modeling Data
Chapter 9 Group Project
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises (Chapters 1–9)
10. Conic Sections and Systems of Nonlinear Equations
10.1 Distance and Midpoint Formulas; Circles
10.2 The Ellipse
10.3 The Hyperbola
MidChapter Check Point Section 10.1–Section 10.3
10.4 The Parabola; Identifying Conic Sections
10.5 Systems of Nonlinear Equations in Two Variables
Chapter 10 Group Project
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises (Chapters 1–10)
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Summation Notation
11.2 Arithmetic Sequences
11.3 Geometric Sequences and Series
MidChapter Check Point Section 11.1–Section 11.3
11.4 The Binomial Theorem
Chapter 11 Group Project
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Test
Cumulative Review Exercises (Chapters 1–11)
Appendix
Where Did That Come From? Selected Proofs
Preface
Writing the Third Edition
A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:
I thought about both of these objections in writing every page of the Third Edition.
"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in the Third Edition have been extensively rewritten to make them more accessible. I have paid close attention to ensuring that the amount of detail and depth of coverage is appropriate for an intermediate college algebra course. Every section has been rewritten to contain a better range of simple, intermediate, and challenging examples. Voice balloons allow for more specific annotations in examples, further clarifying procedures and concepts. A more open format gives the book a less crowded look than the Second Edition.
"The applications are not interesting." One of the things I enjoy most about teaching in a large urban community college is the diversity of whomy students are and what interests them. Realworld data that celebrate this variety are used to bring relevance to examples, discussions, and applications. Most data from the previous edition have been replaced to include data that extend as far up to the present as possible. Updated realworld data were selected on the basis of being interesting and intriguing to students. By connecting algebra to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.
New to the Third Edition
The Third Edition is a significant revision of the Second Edition, with increased emphasis on the relevance of algebra in everyday aspects of students' lives. In addition to the book's new open look, the expanded explanations, and the updated realworld data, you will find the following new features in the Third Edition.
Preserved and Expanded from the Second Edition. The features described below that helped make the Second Edition so popular continue in the Third Edition.
Supplements for the instructor
Printed Resources
Annotated Instructor's Edition (0130614521)
• Answers to exercises on the same text page or in Graphing Answer Section.
• Graphing Answer Section contains answers to exercises requiring graphical solutions.
Instructor's Solutions Manual (0130342912)
• Stepbystep solutions for every evennumbered section exercise.
• Stepbystep solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.
Instructor's Resource Manual (0130342807)
• Notes to the Instructor
• Eight Chapter Tests per chapter (5 free response, 3 multiple choice)
• Eight Final Exams ( 4 free response, 4 multiple choice)
• Twenty additional exercises per section for added test exercises or worksheets.
• Answers to all items
Media Resources
TestGenEQ with QuizMasterEQ (CD ROM for IBM and Macintosh 0130619361)
• Algorithmically driven, text specific testing program.
• Networkable for administering tests and capturing grades online.
• Edit or add your own questions to create a nearly unlimited number of tests and worksheets.
• Use the new "Function Plotter" to create graphs.
• Tests can be easily exported to HTML so they can be posted to the Web.
Computerized Tutorial Software Course Management System
MathPro Explorer 4.0
• Network version for IBM and Macintosh
• Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.
• Includes an email function for networked users, enabling instructors to send a message to a specific student or to an entire group.
• Network based reports and summaries for a class or student and for cumulative or selected scores are available.
MathPro 5
• Anytime. Anywhere.
• Online tutorial with enhanced class and student management features.
• Integration of TestGenEQ allows for testing to operate within the tutorial environment.
• Course management tracking of both tutorial and testing activity.
Online Options for Distance Learning
WebCT/Blackboard/CourseCompass
• Prentice Hall offers three different online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.
Supplements for the Student
Printed Resources
Student Solutions Manual (0130342890)
• Stepbystep solutions for every oddnumbered section exercise.
• Stepbystep solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.
How to Study Mathematics
• Have your instructor contact the local Prentice Hall sales representative. Math on the Internet: A Student's Guide
• Have your instructor contact the local Prentice Hall sales representative.
Media Resources
Computerized Tutorial Software
MathPro Explorer 4.0
• Keyed to each section of the text for textspecific tutorial exercises and instruction.
• Warmup exercises and graded Practice Problems.
• Video clips show a problem being explained and worked out on the board.
• Algorithmically generated exercises. Online help, glossary and summary of scores.
MathPro 5Anytime. Anywhere.
• Enhanced, Internetbased version of Prentice Hall's popular tutorial software.
Lecture Videos
• Keyed to each section of the text.
Digitized Lecture Videos on CD.
• Have your instructor contact the local Prentice Hall sales representative.
Prentice Hall Tutor Center
• Provides oneonone tutorial assistance by phone, email, or fax.
Companion Website
• Offers Warmups, Real World Activities and Chapter Quizzes.
• Email results to your instructor.
• Destination links provide additional opportunities to explore other related sites.
To The Student
I've written this book so that you can learn about the power of algebra and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and workedout examples that present solutions in a stepbystep manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra to your life to make your learning experience both interesting and relevant.
As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:
1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed.
2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These workedout examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific workedout examples.
3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.
4. Prepare for chapter exams. After completing a chapter, study the summary chart, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book.
5. Use the supplements available with this book. A solutions manual containing workedout solutions to the book's oddnumbered exercises, all review exercises, and all Check Points, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.
I wrote this book in Point Reyes National Seashore, 40 miles north of San Francisco. The park consists of 75,000 acres with miles of pristine surfwashed beaches, forested ridges, and bays bordered by white cliffs. It was my hope to convey the beauty and excitement of mathematics using nature's unspoiled beauty as a source of inspiration and creativity. Enjoy the pages that follow as you empower yourself with the algebra needed to succeed in college, your career, and in your life.
Regards,
Bob
Robert Blitzer