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Graphical Approach to College Algebra, A
ISBN: 9780321356895 | 0321356896
Edition: 4thFormat: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2007
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This edition has evolved to address the needs of today ' s student.& While maintaining its unique table& of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions. & It continues to incorporate an open design, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching.
| Preface | p. xii |
| Linear Functions, Equations, and Inequalities | p. 1 |
| Real Numbers and the Rectangular Coordinate System | p. 2 |
| Sets of Real Numbers | |
| The Rectangular Coordinate System | |
| Viewing Windows | |
| Roots | |
| Distance and Midpoint Formulas | |
| Introduction to Relations and Functions | p. 12 |
| Set-Builder Notation and Inte... MORE | |
| Relations, Domain, and Range | |
| Functions | |
| Tables | |
| Function Notation | |
| Reviewing Basic Concepts (Sections 1.1 and 1.2) | p. 22 |
| Linear Functions | p. 23 |
| Basic Concepts about Linear Functions | |
| Slope of a Line | |
| Slope-Intercept Form of the Equation of a Line | |
| Equations of Lines and Linear Models | p. 36 |
| Point-Slope Form of the Equation of a Line | |
| Standard Form of the Equation of a Line | |
| Parallel and Perpendicular Lines | |
| Linear Models and Regression | |
| Reviewing Basic Concepts (Sections 1.3 and 1.4) | p. 50 |
| Linear Equations and Inequalities | p. 51 |
| Solving Linear Equations | |
| Graphical Approaches to Solving Linear Equations | |
| Identities and Contradictions | |
| Solving Linear Inequalities | |
| Graphical Approaches to Solving Linear Inequalities | |
| Three-Part Inequalities | |
| Applications of Linear Functions | p. 66 |
| Problem-Solving Strategies | |
| Applications of Linear Equations | |
| Break-Even Analysis | |
| Direct Variation | |
| Formulas | |
| Reviewing Basic Concepts (Sections 1.5 and 1.6) | p. 78 |
| Chapter 1 Summary | p. 79 |
| Chapter 1 Review Exercises | p. 82 |
| Chapter 1 Test | p. 87 |
| Chapter 1 Project Predicting Heights and Weights of Athletes | p. 88 |
| Analysis of Graphs of Functions | p. 89 |
| Graphs of Basic Functions and Relations; Symmetry | p. 90 |
| Continuity | |
| Increasing and Decreasing Functions | |
| The Identity Function | |
| The Squaring Function and Symmetry with Respect to the y-Axis | |
| The Cubing Function and Symmetry with Respect to the Origin | |
| The Square Root and Cube Root Functions | |
| The Absolute Value Function | |
| The Relation x = y[superscript 2] and Symmetry with Respect to the x-Axis | |
| Even and Odd Functions | |
| Vertical and Horizontal Shifts of Graphs | p. 103 |
| Vertical Shifts | |
| Horizontal Shifts | |
| Combinations of Vertical and Horizontal Shifts | |
| Effects of Shifts on Domain and Range | |
| Horizontal Shifts Applied to Equations for Modeling | |
| Stretching, Shrinking, and Reflecting Graphs | p. 113 |
| Vertical Stretching | |
| Vertical Shrinking | |
| Horizontal Stretching and Shrinking | |
| Reflecting across an Axis | |
| Combining Transformations of Graphs | |
| Reviewing Basic Concepts (Sections 2.1-2.3) | p. 125 |
| Absolute Value Functions: Graphs, Equations, Inequalities, and Applications | p. 127 |
| The Graph of y = [vertical bar]f(x)[vertical bar] | |
| Properties of Absolute Value | |
| Equations and Inequalities Involving Absolute Value | |
| An Application Involving Absolute Value | |
| Piecewise-Defined Functions | p. 138 |
| Graphing Piecewise-Defined Functions | |
| The Greatest Integer Function | |
| Applications of Piecewise-Defined Functions | |
| Operations and Composition | p. 149 |
| Operations on Functions | |
| The Difference Quotient | |
| Composition of Functions | |
| Applications of Operations and Composition | |
| Reviewing Basic Concepts (Sections 2.4-2.6) | p. 162 |
| Chapter 2 Summary | p. 163 |
| Chapter 2 Review Exercises | p. 166 |
| Chapter 2 Test | p. 169 |
| Chapter 2 Project Modeling the Movement of a Cold Front | p. 171 |
| Polynomial Functions | p. 173 |
| Complex Numbers | p. 174 |
| The Number i | |
| Operations with Complex Numbers | |
| Quadratic Functions and Graphs | p. 181 |
| Completing the Square | |
| Graphs of Quadratic Functions | |
| Vertex Formula | |
| Extreme Values | |
| Applications and Quadratic Models | |
| Quadratic Equations and Inequalities | p. 194 |
| Zero-Product Property | |
| Solving x[superscript 2] = k | |
| Quadratic Formula and the Discriminant | |
| Solving Quadratic Equations | |
| Solving Quadratic Inequalities | |
| Formulas Involving Quadratics | |
| Another Quadratic Model | |
| Reviewing Basic Concepts (Sections 3.1-3.3) | p. 208 |
| Further Applications of Quadratic Functions and Models | p. 208 |
| Applications of Quadratic Functions | |
| Quadratic Models | |
| Higher-Degree Polynomial Functions and Graphs | p. 218 |
| Cubic Functions | |
| Quartic Functions | |
| Extrema | |
| End Behavior | |
| x-Intercepts (Real Zeros) | |
| Comprehensive Graphs | |
| Curve Fitting and Polynomial Models | |
| Reviewing Basic Concepts (Sections 3.4 and 3.5) | p. 231 |
| Topics in the Theory of Polynomial Functions (I) | p. 231 |
| Intermediate Value Theorem | |
| Division of Polynomials and Synthetic Division | |
| Remainder and Factor Theorems | |
| Topics in the Theory of Polynomial Functions (II) | p. 240 |
| Complex Zeros and the Fundamental Theorem of Algebra | |
| Number of Zeros | |
| Rational Zeros Theorem | |
| Descartes' Rule of Signs | |
| Boundedness Theorem | |
| Polynomial Equations and Inequalities; Further Applications and Models | p. 251 |
| Polynomial Equations and Inequalities | |
| Complex nth Roots | |
| Applications and Polynomial Models | |
| Reviewing Basic Concepts (Sections 3.6-3.8) | p. 259 |
| Chapter 3 Summary | p. 260 |
| Chapter 3 Review Exercises | p. 263 |
| Chapter 3 Test | p. 267 |
| Chapter 3 Project Creating a Social Security Polynomial | p. 268 |
| Rational, Power, and Root Functions | p. 270 |
| Rational Functions and Graphs | p. 271 |
| The Reciprocal Function | |
| The Rational Function Defined by f(x) = 1/x[superscript 2] | |
| More on Graphs of Rational Functions | p. 277 |
| Vertical and Horizontal Asymptotes | |
| Graphing Techniques | |
| Oblique Asymptotes | |
| Graphs with Points of Discontinuity | |
| Rational Equations, Inequalities, Applications, and Models | p. 291 |
| Solving Rational Equations and Inequalities | |
| Applications and Models of Rational Functions | |
| Inverse Variation | |
| Combined and Joint Variation | |
| Reviewing Basic Concepts (Sections 4.1-4.3) | p. 305 |
| Functions Defined by Powers and Roots | p. 306 |
| Power and Root Functions | |
| Modeling Using Power Functions | |
| Graphs of f(x) = [characters not reproducible] | |
| Graphing Circles and Horizontal Parabolas Using Root Functions | |
| Equations, Inequalities, and Applications Involving Root Functions | p. 318 |
| Equations and Inequalities | |
| An Application of Root Functions | |
| Reviewing Basic Concepts (Sections 4.4 and 4.5) | p. 328 |
| Chapter 4 Summary | p. 329 |
| Chapter 4 Review Exercises | p. 331 |
| Chapter 4 Test | p. 335 |
| Chapter 4 Project How Rugged Is Your Coastline? | p. 336 |
| Inverse, Exponential, and Logarithmic Functions | p. 338 |
| Inverse Functions | p. 339 |
| Inverse Operations | |
| One-to-One Functions | |
| Inverse Functions and Their Graphs | |
| Equations of Inverse Functions | |
| An Application of Inverse Functions | |
| Exponential Functions | p. 350 |
| Real-Number Exponents | |
| Graphs of Exponential Functions | |
| Exponential Equations (Type 1) | |
| Compound Interest | |
| The Number e and Continuous Compounding | |
| An Application of Exponential Functions | |
| Logarithms and Their Properties | p. 363 |
| Definition of Logarithm | |
| Common Logarithms | |
| Natural Logarithms | |
| Properties of Logarithms | |
| Change-of-Base Rule | |
| Reviewing Basic Concepts (Sections 5.1-5.3) | p. 373 |
| Logarithmic Functions | p. 374 |
| Graphs of Logarithmic Functions | |
| Applying Earlier Work to Logarithmic Functions | |
| A Logarithmic Model | |
| Exponential and Logarithmic Equations and Inequalities | p. 384 |
| Exponential Equations and Inequalities (Type 2) | |
| Logarithmic Equations and Inequalities | |
| Equations and Inequalities Involving Both Exponentials and Logarithms | |
| Formulas Involving Exponentials and Logarithms | |
| Reviewing Basic Concepts (Sections 5.4 and 5.5) | p. 393 |
| Further Applications and Modeling with Exponential and Logarithmic Functions | p. 394 |
| Physical Science Applications | |
| Financial Applications | |
| Biological and Medical Applications | |
| Modeling Data with Exponential and Logarithmic Functions | |
| Chapter 5 Summary | p. 408 |
| Chapter 5 Review Exercises | p. 411 |
| Chapter 5 Test | p. 414 |
| Chapter 5 Project Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models) | p. 415 |
| Analytic Geometry | p. 417 |
| Circles and Parabolas | p. 418 |
| Conic Sections | |
| Equations and Graphs of Circles | |
| Equations and Graphs of Parabolas | |
| Translations of Parabolas | |
| An Application of Parabolas | |
| Ellipses and Hyperbolas | p. 432 |
| Equations and Graphs of Ellipses | |
| Translations of Ellipses | |
| An Application of Ellipses | |
| Equations and Graphs of Hyperbolas | |
| Translations of Hyperbolas | |
| Reviewing Basic Concepts (Sections 6.1 and 6.2) | p. 445 |
| Summary of the Conic Sections | p. 445 |
| Characteristics | |
| Identifying Conic Sections | |
| Eccentricity | |
| Parametric Equations | p. 454 |
| Graphs of Parametric Equations and Their Rectangular Equivalents | |
| Alternative Forms of Parametric Equations | |
| An Application of Parametric Equations | |
| Reviewing Basic Concepts (Sections 6.3 and 6.4) | p. 458 |
| Chapter 6 Summary | p. 459 |
| Chapter 6 Review Exercises | p. 461 |
| Chapter 6 Test | p. 463 |
| Chapter 6 Project Modeling the Path of a Bouncing Ball | p. 464 |
| Systems of Equations and Inequalities; Matrices | p. 466 |
| Systems of Equations | p. 467 |
| Linear Systems | |
| Substitution Method | |
| Elimination Method | |
| Special Systems | |
| Nonlinear Systems | |
| Applications of Systems | |
| Solution of Linear Systems in Three Variables | p. 480 |
| Geometric Considerations | |
| Analytic Solution of Systems in Three Variables | |
| Applications of Systems | |
| Curve Fitting Using a System | |
| Solution of Linear Systems by Row Transformations | p. 488 |
| Matrix Row Transformations | |
| Row Echelon Method | |
| Reduced Row Echelon Method | |
| Special Cases | |
| An Application of Matrices | |
| Reviewing Basic Concepts (Sections 7.1-7.3) | p. 499 |
| Matrix Properties and Operations | p. 500 |
| Terminology of Matrices | |
| Operations on Matrices | |
| Applying Matrix Algebra | |
| Determinants and Cramer's Rule | p. 513 |
| Determinants of 2 x 2 Matrices | |
| Determinants of Larger Matrices | |
| Derivation of Cramer's Rule | |
| Using Cramer's Rule to Solve Systems | |
| Solution of Linear Systems by Matrix Inverses | p. 524 |
| Identity Matrices | |
| Multiplicative Inverses of Square Matrices | |
| Using Determinants to Find Inverses | |
| Solving Linear Systems Using Inverse Matrices | |
| Curve Fitting Using a System | |
| Reviewing Basic Concepts (Sections 7.4-7.6) | p. 536 |
| Systems of Inequalities and Linear Programming | p. 537 |
| Solving Linear Inequalities | |
| Solving Systems of Inequalities | |
| Linear Programming | |
| Partial Fractions | p. 547 |
| Decomposition of Rational Expressions | |
| Distinct Linear Factors | |
| Repeated Linear Factors | |
| Distinct Linear and Quadratic Factors | |
| Repeated Quadratic Factors | |
| Reviewing Basic Concepts (Sections 7.7 and 7.8) | p. 554 |
| Chapter 7 Summary | p. 554 |
| Chapter 7 Review Exercises | p. 557 |
| Chapter 7 Test | p. 561 |
| Chapter 7 Project Finding a Polynomial Whose Graph Passes through Any Number of Given Points | p. 562 |
| Further Topics in Algebra | p. 565 |
| Sequences and Series | p. 566 |
| Sequences | |
| Series and Summation Notation | |
| Summation Properties | |
| Arithmetic Sequences and Series | p. 576 |
| Arithmetic Sequences | |
| Arithmetic Series | |
| Geometric Sequences and Series | p. 584 |
| Geometric Sequences | |
| Geometric Series | |
| Infinite Geometric Series | |
| Annuities | |
| Reviewing Basic Concepts (Sections 8.1-8.3) | p. 594 |
| The Binomial Theorem | p. 595 |
| A Binomial Expansion Pattern | |
| Pascal's Triangle | |
| n-Factorial | |
| Binomial Coefficients | |
| The Binomial Theorem | |
| rth Term of a Binomial Expansion | |
| Mathematical Induction | p. 602 |
| Proof by Mathematical Induction | |
| Proving Statements | |
| Generalized Principle of Mathematical Induction | |
| Proof of the Binomial Theorem | |
| Reviewing Basic Concepts (Sections 8.4 and 8.5) | p. 608 |
| Counting Theory | p. 608 |
| Fundamental Principle of Counting | |
| Permutations | |
| Combinations | |
| Distinguishing between Permutations and Combinations | |
| Probability | p. 617 |
| Basic Concepts | |
| Complements and Venn Diagrams | |
| Odds | |
| Union of Two Events | |
| Binomial Probability | |
| Reviewing Basic Concepts (Sections 8.6 and 8.7) | p. 626 |
| Chapter 8 Summary | p. 627 |
| Chapter 8 Review Exercises | p. 631 |
| Chapter 8 Test | p. 633 |
| Chapter 8 Project Using Experimental Probabilities to Simulate Family Makeup | p. 634 |
| Reference: Basic Algebraic Concepts | p. 637 |
| Review of Exponents and Polynomials | p. 638 |
| Rules for Exponents | |
| Terminology for Polynomials | |
| Adding and Subtracting Polynomials | |
| Multiplying Polynomials | |
| Review of Factoring | p. 644 |
| Factoring Out the Greatest Common Factor | |
| Factoring by Grouping | |
| Factoring Trinomials | |
| Factoring Special Products | |
| Factoring by Substitution | |
| Review of Rational Expressions | p. 651 |
| Domain of a Rational Expression | |
| Lowest Terms of a Rational Expression | |
| Multiplying and Dividing Rational Expressions | |
| Adding and Subtracting Rational Expressions | |
| Complex Fractions | |
| Review of Negative and Rational Exponents | p. 659 |
| Negative Exponents and the Quotient Rule | |
| Rational Exponents | |
| Review of Radicals | p. 665 |
| Radical Notation | |
| Rules for Radicals | |
| Simplifying Radicals | |
| Operations with Radicals | |
| Rationalizing Denominators | |
| Chapter R Test | p. 673 |
| Geometry Formulas | p. 674 |
| Deciding Which Model Best Fits a Set of Data | p. 676 |
| Answers to Selected Exercises | p. 1 |
| Index of Applications | p. 1 |
| Index | p. 5 |
| Table of Contents provided by Ingram. All Rights Reserved. |
