Preface | p. xiv |

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 Interval Notation | |

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 | p. 174 |

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 | |

Analyttic 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 |

Trigonometric Functions and Applications | p. 565 |

Angles and Their Measures | p. 566 |

Basic Terminology | |

Degree Measure | |

Standard Position and Coterminal Angles | |

Radian Measure | |

Arc Lengths and Areas of Sectors | |

Angular and Linear Speed | |

Trigonometric Functions and Fundamental Identities | p. 582 |

Trigonometric Functions | |

Quadrantal Angles | |

Reciprocal Identities | |

Signs and Ranges of Function Values | |

Pythagorean Identities | |

Quotient Identities | |

An Application of Trigonometric Functions | |

Reviewing Basic Concepts (Sections 8.1 and 8.2) | p. 595 |

Evaluating Trigonometric Functions | p. 596 |

Definitions of the Trigonometric Functions | |

Trigonometric Function Values of Special Angles | |

Cofunction Identities | |

Reference Angles | |

Special Angles as Reference Angles | |

Finding Function Values with a Calculator | |

Finding Angle Measures | |

Applications of Right Triangles | p. 608 |

Significant Digits | |

Solving Triangles | |

Angles of Elevation or Depression | |

Bearing | |

Further Applications of Trigonometric Functions | |

Reviewing Basic Concepts (Sections 8.3 and 8.4) | p. 620 |

The Circular Functions | p. 620 |

Circular Functions | |

Applications of Circular Functions | |

Graphs of the Sine and Cosine Functions | p. 629 |

Periodic Functions | |

Graph of the Sine Function | |

Graph of the Cosine Function | |

Graphing Techniques, Amplitude, and Period | |

Translations | |

Determining a Trigonometric Model Using Curve Fitting | |

Reviewing Basic Concepts (Sections 8.5 and 8.6) | p. 646 |

Graphs of the Other Circular Functions | p. 646 |

Graphs of the Cosecant and Secant Functions | |

Graphs of the Tangent and Cotangent Functions | |

Addition of Ordinates | |

Harmonic Motion | p. 657 |

Simple Harmonic Motion | |

Damped Oscillatory Motion | |

Reviewing Basic Concepts (Sections 8.7 and 8.8) | p. 660 |

Chapter 8 Summary | p. 661 |

Chapter 8 Review Exercises | p. 665 |

Chapter 8 Test | p. 670 |

Chapter 8 Project: Modeling Sunset Times | p. 671 |

Trigonometric Identities and Equations | p. 672 |

Trigonometric Identities | p. 673 |

Fundamental Identities | |

Using the Fundamental Identities | |

Verifying Identities | |

Sum and Difference Identities | p. 683 |

Cosine Sum and Difference Identities | |

Sine and Tangent Sum and Difference Identities | |

Reviewing Basic Concepts (Sections 9.1 and 9.2) | p. 692 |

Further Identities | p. 692 |

Double-Number Identities | |

Product-to-Sum and Sum-to-Product Identities | |

Half-Number Identities | |

The Inverse Circular Functions | p. 704 |

Review of Inverse Functions | |

Inverse Sine Function | |

Inverse Cosine Function | |

Inverse Tangent Function | |

Remaining Inverse Trigonometric Functions | |

Inverse Function Values | |

Reviewing Basic Concepts (Sections 9.3 and 9.4) | p. 717 |

Trigonometric Equations and Inequalities (I) | p. 717 |

Equations Solvable by Linear Methods | |

Equations Solvable by Factoring | |

Equations Solvable by the Quadratic Formula | |

Using Trigonometric Identities to Solve Equations | |

Trigonometric Equations and Inequalities (II) | p. 724 |

Equations and Inequalities Involving Multiple-Number Identities | |

Equations and Inequalities Involving Half-Number Identities | |

An Application of Trigonometric Equations | |

Reviewing Basic Concepts (Sections 9.5 and 9.6) | p. 730 |

Chapter 9 Summary | p. 731 |

Chapter 9 Review Exercises | p. 733 |

Chapter 9 Test | p. 736 |

Chapter 9 Project: Modeling a Damped Pendulum | p. 737 |

Applications of Trigonometry; Vectors | p. 739 |

The Law of Sines | p. 740 |

Congruency and Oblique Triangles | |

Derivation of the Law of Sines | |

Applications of Triangles | |

Ambiguous Case | |

The Law of Cosines and Area Formulas | p. 754 |

Derivation of the Law of Cosines | |

Applications of Triangles | |

Area Formulas | |

Vectors and Their Applications | p. 764 |

Basic Terminology | |

Algebraic Interpretation of Vectors | |

Operations with Vectors | |

Dot Product and the Angle between Vectors | |

Applications of Vectors | |

Reviewing Basic Concepts (Sections 10.1-10.3) | p. 777 |

Trigonometric (Polar) Form of Complex Numbers | p. 778 |

The Complex Plane and Vector Representation | |

Trigonometric (Polar) Form | |

Products of Complex Numbers in Trigonometric Form | |

Quotients of Complex Numbers in Trigonometric Form | |

Powers and Roots of Complex Numbers | p. 787 |

Powers of Complex Numbers (De Moivre's Theorem) | |

Roots of Complex Numbers | |

Reviewing Basic Concepts (Sections 10.4 and 10.5) | p. 793 |

Polar Equations and Graphs | p. 793 |

Polar Coordinate System | |

Graphs of Polar Equations | |

Classifying Polar Equations | |

Converting Equations | |

More Parametric Equations | p. 804 |

Parametric Equations with Trigonometric Functions | |

The Cycloid | |

Applications of Parametric Equations | |

Reviewing Basic Concepts (Sections 10.6 and 10.7) | p. 811 |

Chapter 10 Summary | p. 811 |

Chapter 10 Review Exercises | p. 814 |

Chapter 10 Test | p. 817 |

Chapter 10 Project: When Is a Circle Really a Polygon? | p. 818 |

Further Topics in Algebra | p. 820 |

Sequences and Series | p. 821 |

Sequences | |

Series and Summation Notation | |

Summation Properties | |

Arithmetic Sequences and Series | p. 831 |

Arithmetic Sequences | |

Arithmetic Series | |

Geometric Sequences and Series | p. 839 |

Geometric Sequences | |

Geometric Series | |

Infinite Geometric Series | |

Annuities | |

Reviewing Basic Concepts (Sections 11.1-11.3) | p. 849 |

The Binomial Theorem | p. 850 |

A Binomial Expansion Pattern | |

Pascal's Triangle | |

n-Factorial | |

Binomial Coefficients | |

The Binomial Theorem | |

rth Term of a Binomial Expansion | |

Mathematical Induction | p. 857 |

Proof by Mathematical Induction | |

Proving Statements | |

Generalized Principle of Mathematical Induction | |

Proof of the Binomial Theorem | |

Reviewing Basic Concepts (Sections 11.4 and 11.5) | p. 863 |

Counting Theory | p. 863 |

Fundamental Principle of Counting | |

Permutations | |

Combinations | |

Distinguishing between Permutations and Combinations | |

Probability | p. 872 |

Basic Concepts | |

Complements and Venn Diagrams | |

Odds | |

Union of Two Events | |

Binomial Probability | |

Reviewing Basic Concepts (Sections 11.6 and 11.7) | p. 881 |

Chapter 11 Summary | p. 882 |

Chapter 11 Review Exercises | p. 886 |

Chapter 11 Test | p. 888 |

Chapter 11 Project: Using Experimental Probabilities to Simulate Family Makeup | p. 889 |

Reference: Basic Algebraic Concepts | p. 892 |

Review of Exponents and Polynomials | p. 893 |

Rules for Exponents | |

Terminology for Polynomials | |

Adding and Subtracting Polynomials | |

Multiplying Polynomials | |

Review of Factoring | p. 899 |

Factoring Out the Greatest Common Factor | |

Factoring by Grouping | |

Factoring Trinomials | |

Factoring Special Products | |

Factoring by Substitution | |

Review of Rational Expressions | p. 906 |

Domain of a Rational Expression | |

Lowest Terms of a Rational Expression | |

Multipling and Dividing Rational Expressions | |

Adding and Subtracting Rational Expressions | |

Complex Fractions | |

Review of Negative and Rational Exponents | p. 914 |

Negative Exponents and the Quotient Rule | |

Rational Exponents | |

Review of Radicals | p. 920 |

Radical Notation | |

Rules for Radicals | |

Simplifying Radicals | |

Operations with Radicals | |

Rationalizing Denominators | |

Chapter R Test | p. 928 |

Geometry Formulas | p. 929 |

Deciding Which Model Best Fits a Set of Data | p. 931 |

Vectors in Space | p. 936 |

Polar Form of Conic Sections | p. 942 |

Rotation of Axes | p. 946 |

Answers to Selected Exercises | p. 1 |

Index of Applications | p. 1 |

Index | p. 5 |

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