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College Algebra with Modeling and Visualization

by: Rockswold, Gary K.

College Algebra with Modeling and Visualization

by: Rockswold, Gary K.

ISBN 13:
9780321279088
ISBN 10:
0321279085
Edition: 3rd
Format: Hardcover
Copyright: 01/01/2006
Publisher: Addison Wesley
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Summary

Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the reader to succeed. Introduction to Functions and Graphs. Linear Functions and Equations. Quadratic Functions and Equations. Nonlinear Functions and Equations. Exponential and Logarithmic Functions. Systems of Equations and Inequalities. Conic Sections. Further Topics in Algebra. Basic Concepts From Algebra and Geometry. For all readers interested in college algebra.

Preface

xiii

Introduction To Functions and Graphs

(71)

Numbers, Data, and Problem Solving

(12)

Sets of Numbers

Scientific Notation

Problem Solving

Visualization of Data

(15)

One-Variable Data

Two-Variable Data

The Distance Formula

The Midpoint Formula

Graphing with a Calculator (Optional)

Checking Basic Concepts for Sections 1.1 and 1.2

(1)

Functions and Their Representations

(17)

Basic Concepts

Representations of Functions

Formal Definition of a Function

Graphing Calculators and Functions (Optional)

Identifying Functions

Types of Functions and Their Rates of Change

(26)

Constant Functions

Linear Functions

Slope as a Rate of Change

Nonlinear Functions

Average Rate of Change

The Difference Quotient

Checking Basic Concepts for Sections 1.3 and 1.4

(1)

Summary

(4)

Review Exercises

(4)

Extended and Discovery Exercises

(2)

Linear Functions and Equations

(99)

Linear Functions and Models

(14)

Exact and Approximate Models

Representations of Linear Functions

Modeling with Linear Functions

Linear Regression (Optional)

Equations of Lines

(19)

Forms for Equations of Lines

Determining Intercepts

Horizontal, Vertical, Parallel, and Perpendicular Lines

Modeling Data (Optional)

Interpolation and Extrapolation

Direct Variation

Checking Basic Concepts for Sections 2.1 and 2.2

106

(1)

Linear Equations

106

(17)

Equations

Symbolic Solutions

Graphical and Numerical Solutions

Problem-Solving Strategies

Linear Inequalities

123

(17)

Inequalities

Interval Notation

Techniques for Solving Inequalities

Compound Inequalities

Checking Basic Concepts for Sections 2.3 and 2.4

139

(1)

Piecewise-Defined Functions

140

(31)

Evaluating and Graphing Piecewise-Defined Functions

The Greatest Integer Function

The Absolute Value Function

Equations and Inequalities Involving Absolute Values

Checking Basic Concepts for Section 2.5

158

(1)

Summary

158

(4)

Review Exercises

162

(4)

Extended and Discovery Exercises

166

(1)

Cumulative Review Exercises

167

(4)

Quadratic Functions and Equations

171

(70)

Quadratic Functions and Models

172

(17)

Basic Concepts

Completing the Square and the Vertex Formula

Applications and Models

Quadratic Regression (Optional)

Quadratic Equations and Problem Solving

189

(17)

Basic Concepts

Solving Quadratic Equations

Problem Solving

Checking Basic Concepts for Sections 3.1 and 3.2

205

(1)

Quadratic Inequalities

206

(10)

Graphical Solutions

Symbolic Solutions

Transformations of Graphs

216

(25)

Vertical and Horizontal Translations

Stretching and Shrinking

Reflection of Graphs

Combining Transformations

Modeling with Transformations (Optional)

Checking Basic Concepts for Sections 3.3 and 3.4

233

(1)

Summary

234

(3)

Review Exercises

237

(2)

Extended and Discovery Exercises

239

(2)

Nonlinear Functions and Equations

241

(122)

Nonlinear Functions and Their Graphs

242

(15)

Polynomial Functions

Increasing and Decreasing Functions

Extrema of Nonlinear Functions

Symmetry

Polynomial Functions and Models

257

(17)

Graphs of Polynomial Functions

Piecewise-Defined Polynomial Functions

Polynomial Regression (Optional)

Checking Basic Concepts for Sections 4.1 and 4.2

273

(1)

Real Zeros of Polynomial Functions

274

(19)

Division of Polynomials

Factoring Polynomials

Graphs and Multiple Zeros

Rational Zeros

Polynomial Equations

The Fundamental Theorem of Algebra

293

(12)

Complex Numbers

Quadratic Equations with Complex Solutions

Fundamental Theorem of Algebra

Polynomial Equations with Complex Solutions

Checking Basic Concepts for Sections 4.3 and 4.4

305

(1)

Rational Functions and Models

305

(20)

Rational Functions

Vertical Asymptotes

Horizontal Asymptotes

Identifying Asymptotes

Rational Equations

Variation

Polynomial and Rational Inequalities

325

(9)

Polynomial Inequalities

Rational Inequalities

Checking Basic Concepts for Sections 4.5 and 4.6

334

(1)

Power Functions and Radical Equations

334

(29)

Rational Exponents and Radical Notation

Power Functions and Models

Equations Involving Rational Exponents

Equations Involving Radicals

Power Regression (Optional)

Checking Basic Concepts for Section 4.7

346

(1)

Summary

347

(5)

Review Exercises

352

(5)

Extended and Discovery Exercises

357

(1)

Cumulative Review Exercises

358

(5)

Exponential and Logarithmic Functions

363

(111)

Combining Functions

364

(18)

Arithmetic Operations on Functions

Composition of Functions

Inverse Functions and Their Representations

382

(17)

Inverse Operations

One-to-One Functions

Symbolic Representations of Inverse Functions

Other Representations of Inverse Functions

Checking Basic Concepts for Sections 5.1 and 5.2

399

(1)

Exponential Functions and Models

399

(20)

Linear and Exponential Growth

Exponential Models

Compound Interest

The Natural Exponential Function

Logarithmic Functions and Models

419

(17)

The Common Logarithmic Function

Basic Equations

Logarithms with Other Bases

General Logarithmic Equations

Checking Basic Concepts for Sections 5.3 and 5.4

435

(1)

Properties of Logarithms

436

(8)

Basic Properties of Logarithms

Change of Base Formula

Exponential and Logarithmic Equations

444

(13)

Exponential Equations

Logarithmic Equations

Checking Basic Concepts for Sections 5.5 and 5.6

457

(1)

Constructing Nonlinear Models

457

(17)

Exponential Model

Logarithmic Model

Logistic Model

Checking Basic Concepts for Section 5.7

464

(1)

Summary

464

(4)

Review Exercises

468

(4)

Extended and Discovery Exercises

472

(2)

Systems of Equations and Inequalities

474

(110)

Functions and Equations in Two Variables

475

(15)

Functions of Two Variables

Systems of Equations

The Method of Substitution

Graphical and Numerical Methods

Joint Variation

Systems of Equations and Inequalities in Two Variables

490

(18)

Types of Linear Systems in Two Variables

The Elimination Method

Systems of Linear and Nonlinear Inequalities

Linear Programming

Checking Basic Concepts for Sections 6.1 and 6.2

508

(1)

Systems of Linear Equations in Three Variables

508

(8)

Basic Concepts

Solving with Elimination and Substitution

Systems of Linear and Nonlinear Inequalities

Systems with Infinitely Many Solutions

Solutions to Linear Systems Using Matrices

516

(17)

Representing Systems of Linear Equations with Matrices

Row-Echelon Form

Gaussian Elimination

Solving Systems of Linear Equations with Technology (Optional)

Checking Basic Concepts for Sections 6.3 and 6.4

532

(1)

Properties and Applications of Matrices

533

(14)

Matrix Notation

Sums, Differences, and Scalar Multiples of Matrices

Matrix Products

Technology and Matrices (Optional)

Inverses of Matrices

547

(14)

Matrix Inverses

Finding Inverses Symbolically

Representing Linear Systems with Matrix Equations

Solving Linear Systems with Inverses

Checking Basic Concepts for Sections 6.5 and 6.6

560

(1)

Determinants

561

(23)

Definition and Calculation of Determinants

Area of Regions

Cramer's Rule

Limitations on the Method of Cofactors and Cramer's Rule

Checking Basic Concepts for Section 6.7

569

(1)

Summary

570

(4)

Review Exercises

574

(3)

Extended and Discovery Exercises

577

(2)

Cumulative Review Exercises

579

(5)

Conic Sections

584

(43)

Parabolas

585

(10)

Equations and Graphs of Parabolas

Reflective Property of Parabolas

Translations of Parabolas

Ellipses

595

(15)

Equations and Graphs of Ellipses

Reflective Property of Ellipses

Translations of Ellipses

Circles

Solving Systems of Nonlinear Equations and Inequalities

Checking Basic Concepts for Sections 7.1 and 7.2

610

(1)

Hyperbolas

610

(17)

Equations and Graphs of Hyperbolas

Reflective Property of Hyperbolas

Translations of Hyperbolas

Solving Systems of Nonlinear Equations

Checking Basic Concepts for Section 7.3

621

(1)

Summary

622

(2)

Review Exercises

624

(2)

Extended and Discovery Exercises

626

(1)

Further Topics in Algebra

627

Sequences

628

(14)

Basic Concepts

Representations of Sequences

Arithmetic Sequences

Geometric Sequences

Series

642

(16)

Basic Concepts

Arithmetic Series

Geometric Series

Summation Notation

Checking Basic Concepts for Sections 8.1 and 8.2

658

(1)

Counting

658

(11)

Fundamental Counting Principle

Permutations

Combinations

The Binomial Theorem

669

(6)

Derivation of the Binomial Theorem

Pascal's Triangle

Checking Basic Concepts for Sections 8.3 and 8.4

674

(1)

Mathematical Induction

675

(6)

Mathematical Induction

Proving Statements

Generalized Principle of Mathematical Induction

Probability

681

Definition of Probability

Compound Events

Independent and Dependent Events

Checking Basic Concepts for Sections 8.5 and 8.6

694

(1)

Summary

694

(4)

Review Exercises

698

(2)

Extended and Discovery Exercises

700

(1)

Cumulative Review Exercises

701

Reference: Basic Concepts from Algebra and Geometry

(1)

Formulas from Geometry

(9)

Geometric Shapes in a Plane

The Pythagorean Theorem

Three-Dimensional Objects

Similar Triangles

A Summary of Geometric Formulas

Circles

(3)

Equations and Graphs of Circles

Finding the Center and Radius of a Circle

Integer Exponents

(7)

Bases and Positive Exponents

Zero and Negative Exponents

Product, Quotient, and Power Rules

Polynomial Expressions

(7)

Addition and Subtraction of Monomials

Addition and Subtraction of Polynomials

Distributive Properties

Multiplying Polynomials

Some Special Products

Factoring Polynomials

(11)

Common Factors

Factoring by Grouping

Factoring x2 + bx + c

Factoring Trinomials by Grouping

Factoring Trinomials with FOIL

Difference of Two Squares

Perfect Square Trinomials

Sum and Difference of Two Cubes

Rational Expressions

(10)

Simplifying Rational Expressions

Multiplication and Division of Rational Expressions

Least Common Multiples

Common Denominators

Addition and Subtraction of Rational Expressions

Clearing Fractions

Complex Fractions

Radical Notation and Rational Exponents

(7)

Radical Notation

Rational Exponents

Properties of Rational Exponents

Radical Expressions

Product Rule for Radical Expressions

Quotient Rule for Radical Expressions

Addition and Subtraction

Multiplication

Rationalizing the Denominator

Appendix A: A Library of Functions

(3)

Appendix B: Using the Graphing Calculator

Bibliography

(1)

Answers to Selected Exercises

(1)

Index of Applications

(5)

Index

Amazon no longer offers textbook rentals. We do!

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

9780321279088

0321279085

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

9780321279088

0321279085

Summary

Table of Contents

Supplemental Materials

Write a Review

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