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by Judith Beecher, Judith Penna and Marvin Bittinger

Cover type: HardbackEdition: 2ND 05

Copyright: 2005

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

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The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition to helping students visualize the math with side-by-sides, the authors focus on helping students make the connection between x-intercepts, zeros, and solutions, both visually and algebraically.

**Features **

- Functions Early and Integrated--This is the only non-graphing-calculator-required book on the market that introduces functions in Chapter 1 and thus sets BPB apart.
- Algebraic Visual Side-by-Sides--Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these side-by-sides helps students make the connection between the algebraic manipulation and the graphical interpretation.
- Zeros, Solutions, and x -Intercepts Theme-This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
- Technology Connection--Throughout each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to solve and check problems.
- Review Icon--This provides the student with a reference to a related section. The student can then go there to review a concept being used in the current section.
- Study Tips--These consist of occasional, brief reminders in the margin that promote effective study habits.
- Connecting the Concepts--Comprehension is streamlined and retention is maximized when the student views a concept in a visual, rather than paragraph, form. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts of a section or several sections work together.

**New To This Edition **

- Visualizing the Graph--This new feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see "the big picture."
- More Focus on Graphs--Throughout the text, there is an increased focus on graphs and graphing, again reminding students how helpful visualization can be in the discipline of mathematics. In particular, graphing of polynomial functions by hand has been added and emphasized in Section 3.1 at the request of reviewers.
- Reorganization of Material--Section 1.5 has been split into two sections, 1.5 and 1.6. Composition of functions has been moved from Section 4.1 to 1.6, where it appears with the material on the algebra of functions.
- Vocabulary Review--Appearing once in every chapter, in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
- Classify the Function--With a focus on conceptual understanding, students are asked one time per chapter to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set.
- Over 1000 New Exercises--The authors have worked hard to add additional exercises, where needed and often at the request of reviewers, on key topics throughout the text.
- Appendix Covering Basic Concepts from Geometry--New to this edition is an appendix covering basic concepts from geometry that students need to know in order to work with topics pertaining to angles and triangles.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book..

**R. Basic Concepts of Algebra. **

The Real-Number System.

Integer Exponents, Scientific Notation, and Order of Operations.

Addition, Subtraction, and Multiplication of Polynomials.

Factoring.

Rational Expressions.

Radical Notation and Rational Exponents.

**1. Graphs, Functions, and Models. **

Introduction to Graphing.

Functions and Graphs.

Linear Functions, Slope, and Applications.

Equations of Lines and Modeling.

More on Functions.

The Algebra of Functions.

Symmetry and Transformations.

**2. Functions, Equations, and Inequalities. **

Linear Equations, Functions, and Models.

The Complex Numbers.

Quadratic Equations, Functions, and Models.

Analyzing Graphs of Quadratic Functions.

More Equation Solving.

Solving Linear Inequalities.

**3. Polynomial and Rational Functions. **

Polynomial Functions and Models.

Polynomial Division; The Remainder and Factor Theorems.

Theorems about Zeros of Polynomial Functions.

Rational Functions.

Polynomial and Rational Inequalities.

Variation and Applications.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions and Graphs.

Logarithmic Functions and Graphs.

Properties of Logarithmic Functions.

Solving Exponential and Logarithmic Equations.

Applications and Models: Growth and Decay.

**5. Systems of Equations and Matrices. **

Systems of Equations in Two Variables.

Systems of Equations in Three Variables.

Matrices and Systems of Equations.

Matrix Operations.

Inverses of Matrices.

Determinants and Cramer's Rule.

Systems of Inequalities and Linear Programming.

Partial Fractions.

**6. Conic Sections. **

The Parabola.

The Circle and the Ellipse.

The Hyperbola.

Nonlinear Systems of Equations.

**7. Sequences, Series, and Combinatorics. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

Mathematical Induction.

Combinatorics: Permutations.

Combinatorics: Combinations.

The Binomial Theorem.

Probability.

Appendix: Basic Concepts from Geometry

Summary

The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition to helping students visualize the math with side-by-sides, the authors focus on helping students make the connection between x-intercepts, zeros, and solutions, both visually and algebraically.

**Features **

- Functions Early and Integrated--This is the only non-graphing-calculator-required book on the market that introduces functions in Chapter 1 and thus sets BPB apart.
- Algebraic Visual Side-by-Sides--Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these side-by-sides helps students make the connection between the algebraic manipulation and the graphical interpretation.
- Zeros, Solutions, and x -Intercepts Theme-This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
- Technology Connection--Throughout each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to solve and check problems.
- Review Icon--This provides the student with a reference to a related section. The student can then go there to review a concept being used in the current section.
- Study Tips--These consist of occasional, brief reminders in the margin that promote effective study habits.
- Connecting the Concepts--Comprehension is streamlined and retention is maximized when the student views a concept in a visual, rather than paragraph, form. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts of a section or several sections work together.

**New To This Edition **

- Visualizing the Graph--This new feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see "the big picture."
- More Focus on Graphs--Throughout the text, there is an increased focus on graphs and graphing, again reminding students how helpful visualization can be in the discipline of mathematics. In particular, graphing of polynomial functions by hand has been added and emphasized in Section 3.1 at the request of reviewers.
- Reorganization of Material--Section 1.5 has been split into two sections, 1.5 and 1.6. Composition of functions has been moved from Section 4.1 to 1.6, where it appears with the material on the algebra of functions.
- Vocabulary Review--Appearing once in every chapter, in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
- Classify the Function--With a focus on conceptual understanding, students are asked one time per chapter to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set.
- Over 1000 New Exercises--The authors have worked hard to add additional exercises, where needed and often at the request of reviewers, on key topics throughout the text.
- Appendix Covering Basic Concepts from Geometry--New to this edition is an appendix covering basic concepts from geometry that students need to know in order to work with topics pertaining to angles and triangles.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book..

Table of Contents

**R. Basic Concepts of Algebra. **

The Real-Number System.

Integer Exponents, Scientific Notation, and Order of Operations.

Addition, Subtraction, and Multiplication of Polynomials.

Factoring.

Rational Expressions.

Radical Notation and Rational Exponents.

**1. Graphs, Functions, and Models. **

Introduction to Graphing.

Functions and Graphs.

Linear Functions, Slope, and Applications.

Equations of Lines and Modeling.

More on Functions.

The Algebra of Functions.

Symmetry and Transformations.

**2. Functions, Equations, and Inequalities. **

Linear Equations, Functions, and Models.

The Complex Numbers.

Quadratic Equations, Functions, and Models.

Analyzing Graphs of Quadratic Functions.

More Equation Solving.

Solving Linear Inequalities.

**3. Polynomial and Rational Functions. **

Polynomial Functions and Models.

Polynomial Division; The Remainder and Factor Theorems.

Theorems about Zeros of Polynomial Functions.

Rational Functions.

Polynomial and Rational Inequalities.

Variation and Applications.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions and Graphs.

Logarithmic Functions and Graphs.

Properties of Logarithmic Functions.

Solving Exponential and Logarithmic Equations.

Applications and Models: Growth and Decay.

**5. Systems of Equations and Matrices. **

Systems of Equations in Two Variables.

Systems of Equations in Three Variables.

Matrices and Systems of Equations.

Matrix Operations.

Inverses of Matrices.

Determinants and Cramer's Rule.

Systems of Inequalities and Linear Programming.

Partial Fractions.

**6. Conic Sections. **

The Parabola.

The Circle and the Ellipse.

The Hyperbola.

Nonlinear Systems of Equations.

**7. Sequences, Series, and Combinatorics. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

Mathematical Induction.

Combinatorics: Permutations.

Combinatorics: Combinations.

The Binomial Theorem.

Probability.

Appendix: Basic Concepts from Geometry

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Published: 2005

International: No

The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition to helping students visualize the math with side-by-sides, the authors focus on helping students make the connection between x-intercepts, zeros, and solutions, both visually and algebraically.

**Features **

- Functions Early and Integrated--This is the only non-graphing-calculator-required book on the market that introduces functions in Chapter 1 and thus sets BPB apart.
- Algebraic Visual Side-by-Sides--Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these side-by-sides helps students make the connection between the algebraic manipulation and the graphical interpretation.
- Zeros, Solutions, and x -Intercepts Theme-This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
- Technology Connection--Throughout each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to solve and check problems.
- Review Icon--This provides the student with a reference to a related section. The student can then go there to review a concept being used in the current section.
- Study Tips--These consist of occasional, brief reminders in the margin that promote effective study habits.
- Connecting the Concepts--Comprehension is streamlined and retention is maximized when the student views a concept in a visual, rather than paragraph, form. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts of a section or several sections work together.

**New To This Edition **

- Visualizing the Graph--This new feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see "the big picture."
- More Focus on Graphs--Throughout the text, there is an increased focus on graphs and graphing, again reminding students how helpful visualization can be in the discipline of mathematics. In particular, graphing of polynomial functions by hand has been added and emphasized in Section 3.1 at the request of reviewers.
- Reorganization of Material--Section 1.5 has been split into two sections, 1.5 and 1.6. Composition of functions has been moved from Section 4.1 to 1.6, where it appears with the material on the algebra of functions.
- Vocabulary Review--Appearing once in every chapter, in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
- Classify the Function--With a focus on conceptual understanding, students are asked one time per chapter to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set.
- Over 1000 New Exercises--The authors have worked hard to add additional exercises, where needed and often at the request of reviewers, on key topics throughout the text.
- Appendix Covering Basic Concepts from Geometry--New to this edition is an appendix covering basic concepts from geometry that students need to know in order to work with topics pertaining to angles and triangles.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book..

**R. Basic Concepts of Algebra. **

The Real-Number System.

Integer Exponents, Scientific Notation, and Order of Operations.

Addition, Subtraction, and Multiplication of Polynomials.

Factoring.

Rational Expressions.

Radical Notation and Rational Exponents.

**1. Graphs, Functions, and Models. **

Introduction to Graphing.

Functions and Graphs.

Linear Functions, Slope, and Applications.

Equations of Lines and Modeling.

More on Functions.

The Algebra of Functions.

Symmetry and Transformations.

**2. Functions, Equations, and Inequalities. **

Linear Equations, Functions, and Models.

The Complex Numbers.

Quadratic Equations, Functions, and Models.

Analyzing Graphs of Quadratic Functions.

More Equation Solving.

Solving Linear Inequalities.

**3. Polynomial and Rational Functions. **

Polynomial Functions and Models.

Polynomial Division; The Remainder and Factor Theorems.

Theorems about Zeros of Polynomial Functions.

Rational Functions.

Polynomial and Rational Inequalities.

Variation and Applications.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions and Graphs.

Logarithmic Functions and Graphs.

Properties of Logarithmic Functions.

Solving Exponential and Logarithmic Equations.

Applications and Models: Growth and Decay.

**5. Systems of Equations and Matrices. **

Systems of Equations in Two Variables.

Systems of Equations in Three Variables.

Matrices and Systems of Equations.

Matrix Operations.

Inverses of Matrices.

Determinants and Cramer's Rule.

Systems of Inequalities and Linear Programming.

Partial Fractions.

**6. Conic Sections. **

The Parabola.

The Circle and the Ellipse.

The Hyperbola.

Nonlinear Systems of Equations.

**7. Sequences, Series, and Combinatorics. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

Mathematical Induction.

Combinatorics: Permutations.

Combinatorics: Combinations.

The Binomial Theorem.

Probability.

Appendix: Basic Concepts from Geometry