| |

| |

Preface | |

| |

| |

| |

Linear Functions, Equations, and Inequalities | |

| |

| |

| |

Real Numbers and the Rectangular Coordinate System | |

| |

| |

Sets of Real Numbers | |

| |

| |

The Rectangular Coordinate System | |

| |

| |

Viewing Windows | |

| |

| |

Roots | |

| |

| |

Distance and Midpoint Formulas | |

| |

| |

| |

Introduction to Relations and Functions | |

| |

| |

Set-Builder Notation and Interval Notation | |

| |

| |

Relations, Domain, and Range | |

| |

| |

Functions | |

| |

| |

Tables | |

| |

| |

Function Notation | |

| |

| |

Reviewing Basic Concepts (Sections 1.1 and 1.2) | |

| |

| |

| |

Linear Functions | |

| |

| |

Basic Concepts about Linear Functions | |

| |

| |

Slope of a Line | |

| |

| |

Slope-Intercept Form of the Equation of a Line | |

| |

| |

| |

Equations of Lines and Linear Models | |

| |

| |

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) | |

| |

| |

| |

Linear Equations and Inequalities | |

| |

| |

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 | |

| |

| |

Problem-Solving Strategies | |

| |

| |

Applications of Linear Equations | |

| |

| |

Break-Even Analysis | |

| |

| |

Direct Variation | |

| |

| |

Formulas | |

| |

| |

Reviewing Basic Concepts (Sections 1.5 and 1.6) | |

| |

| |

Chapter 1 Summary | |

| |

| |

Chapter 1 Review Exercises | |

| |

| |

Chapter 1 Test | |

| |

| |

Chapter 1 Project Predicting Heights and Weights of Athletes | |

| |

| |

| |

Analysis of Graphs of Functions | |

| |

| |

| |

Graphs of Basic Functions and Relations; Symmetry | |

| |

| |

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 | |

| |

| |

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 | |

| |

| |

Vertical Stretching | |

| |

| |

Vertical Shrinking | |

| |

| |

Horizontal Stretching and Shrinking | |

| |

| |

Reflecting across an Axis | |

| |

| |

Combining Transformations of Graphs | |

| |

| |

Reviewing Basic Concepts (Sections 2.1-2.3) | |

| |

| |

| |

Absolute Value Functions: Graphs, Equations, Inequalities, and Applications | |

| |

| |

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 | |

| |

| |

Graphing Piecewise-Defined Functions | |

| |

| |

The Greatest Integer Function | |

| |

| |

Applications of Piecewise-Defined Functions | |

| |

| |

| |

Operations and Composition | |

| |

| |

Operations on Functions | |

| |

| |

The Difference Quotient | |

| |

| |

Composition of Functions | |

| |

| |

Applications of Operations and Composition | |

| |

| |

Reviewing Basic Concepts (Sections 2.4-2.6) | |

| |

| |

Chapter 2 Summary | |

| |

| |

Chapter 2 Review Exercises | |

| |

| |

Chapter 2 Test | |

| |

| |

Chapter 2 Project Modeling the Movement of a Cold Front | |

| |

| |

| |

Polynomial Functions | |

| |

| |

| |

Complex Numbers | |

| |

| |

The Number i | |

| |

| |

Operations with Complex Numbers | |

| |

| |

| |

Quadratic Functions and Graphs | |

| |

| |

Completing the Square | |

| |

| |

Graphs of Quadratic Functions | |

| |

| |

Vertex Formula | |

| |

| |

Extreme Values | |

| |

| |

Applications and Quadratic Models | |

| |

| |

| |

Quadratic Equations and Inequalities | |

| |

| |

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) | |

| |

| |

| |

Further Applications of Quadratic Functions and Models | |

| |

| |

Applications of Quadratic Functions | |

| |

| |

Quadratic Models | |

| |

| |

| |

Higher-Degree Polynomial Functions and Graphs | |

| |

| |

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) | |

| |

| |

| |

Topics in the Theory of Polynomial Functions (I) | |

| |

| |

Intermediate Value Theorem | |

| |

| |

Division of Polynomials and Synthetic Division | |

| |

| |

Remainder and Factor Theorems | |

| |

| |

| |

Topics in the Theory of Polynomial Functions (II) | |

| |

| |

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 | |

| |

| |

Polynomial Equations and Inequalities | |

| |

| |

Complex nth Roots | |

| |

| |

Applications and Polynomial Models | |

| |

| |

Reviewing Basic Concepts (Sections 3.6-3.8) | |

| |

| |

Chapter 3 Summary | |

| |

| |

Chapter 3 Review Exercises | |

| |

| |

Chapter 3 Test | |

| |

| |

Chapter 3 Project Creating a Social Security Polynomial | |

| |

| |

| |

Rational, Power, and Root Functions | |

| |

| |

| |

Rational Functions and Graphs | |

| |

| |

The Reciprocal Function | |

| |

| |

The Rational Function Defined by f(x) = 1/x[superscript 2] | |

| |

| |

| |

More on Graphs of Rational Functions | |

| |

| |

Vertical and Horizontal Asymptotes | |

| |

| |

Graphing Techniques | |

| |

| |

Oblique Asymptotes | |

| |

| |

Graphs with Points of Discontinuity | |

| |

| |

| |

Rational Equations, Inequalities, Applications, and Models | |

| |

| |

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) | |

| |

| |

| |

Functions Defined by Powers and Roots | |

| |

| |

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 | |

| |

| |

Equations and Inequalities | |

| |

| |

An Application of Root Functions | |

| |

| |

Reviewing Basic Concepts (Sections 4.4 and 4.5) | |

| |

| |

Chapter 4 Summary | |

| |

| |

Chapter 4 Review Exercises | |

| |

| |

Chapter 4 Test | |

| |

| |

Chapter 4 Project How Rugged Is Your Coastline? | |

| |

| |

| |

Inverse, Exponential, and Logarithmic Functions | |

| |

| |

| |

Inverse Functions | |

| |

| |

Inverse Operations | |

| |

| |

One-to-One Functions | |

| |

| |

Inverse Functions and Their Graphs | |

| |

| |

Equations of Inverse Functions | |

| |

| |

An Application of Inverse Functions | |

| |

| |

| |

Exponential Functions | |

| |

| |

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 | |

| |

| |

Definition of Logarithm | |

| |

| |

Common Logarithms | |

| |

| |

Natural Logarithms | |

| |

| |

Properties of Logarithms | |

| |

| |

Change-of-Base Rule | |

| |

| |

Reviewing Basic Concepts (Sections 5.1-5.3) | |

| |

| |

| |

Logarithmic Functions | |

| |

| |

Graphs of Logarithmic Functions | |

| |

| |

Applying Earlier Work to Logarithmic Functions | |

| |

| |

A Logarithmic Model | |

| |

| |

| |

Exponential and Logarithmic Equations and Inequalities | |

| |

| |

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) | |

| |

| |

| |

Further Applications and Modeling with Exponential and Logarithmic Functions | |

| |

| |

Physical Science Applications | |

| |

| |

Financial Applications | |

| |

| |

Biological and Medical Applications | |

| |

| |

Modeling Data with Exponential and Logarithmic Functions | |

| |

| |

Chapter 5 Summary | |

| |

| |

Chapter 5 Review Exercises | |

| |

| |

Chapter 5 Test | |

| |

| |

Chapter 5 Project Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models) | |

| |

| |

| |

Analytic Geometry | |

| |

| |

| |

Circles and Parabolas | |

| |

| |

Conic Sections | |

| |

| |

Equations and Graphs of Circles | |

| |

| |

Equations and Graphs of Parabolas | |

| |

| |

Translations of Parabolas | |

| |

| |

An Application of Parabolas | |

| |

| |

| |

Ellipses and Hyperbolas | |

| |

| |

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) | |

| |

| |

| |

Summary of the Conic Sections | |

| |

| |

Characteristics | |

| |

| |

Identifying Conic Sections | |

| |

| |

Eccentricity | |

| |

| |

| |

Parametric Equations | |

| |

| |

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) | |

| |

| |

Chapter 6 Summary | |

| |

| |

Chapter 6 Review Exercises | |

| |

| |

Chapter 6 Test | |

| |

| |

Chapter 6 Project Modeling the Path of a Bouncing Ball | |

| |

| |

| |

Systems of Equations and Inequalities; Matrices | |

| |

| |

| |

Systems of Equations | |

| |

| |

Linear Systems | |

| |

| |

Substitution Method | |

| |

| |

Elimination Method | |

| |

| |

Special Systems | |

| |

| |

Nonlinear Systems | |

| |

| |

Applications of Systems | |

| |

| |

| |

Solution of Linear Systems in Three Variables | |

| |

| |

Geometric Considerations | |

| |

| |

Analytic Solution of Systems in Three Variables | |

| |

| |

Applications of Systems | |

| |

| |

Curve Fitting Using a System | |

| |

| |

| |

Solution of Linear Systems by Row Transformations | |

| |

| |

Matrix Row Transformations | |

| |

| |

Row Echelon Method | |

| |

| |

Reduced Row Echelon Method | |

| |

| |

Special Cases | |

| |

| |

An Application of Matrices | |

| |

| |

Reviewing Basic Concepts (Sections 7.1-7.3) | |

| |

| |

| |

Matrix Properties and Operations | |

| |

| |

Terminology of Matrices | |

| |

| |

Operations on Matrices | |

| |

| |

Applying Matrix Algebra | |

| |

| |

| |

Determinants and Cramer's Rule | |

| |

| |

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 | |

| |

| |

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) | |

| |

| |

| |

Systems of Inequalities and Linear Programming | |

| |

| |

Solving Linear Inequalities | |

| |

| |

Solving Systems of Inequalities | |

| |

| |

Linear Programming | |

| |

| |

| |

Partial Fractions | |

| |

| |

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) | |

| |

| |

Chapter 7 Summary | |

| |

| |

Chapter 7 Review Exercises | |

| |

| |

Chapter 7 Test | |

| |

| |

Chapter 7 Project Finding a Polynomial Whose Graph Passes through Any Number of Given Points | |

| |

| |

| |

Further Topics in Algebra | |

| |

| |

| |

Sequences and Series | |

| |

| |

Sequences | |

| |

| |

Series and Summation Notation | |

| |

| |

Summation Properties | |

| |

| |

| |

Arithmetic Sequences and Series | |

| |

| |

Arithmetic Sequences | |

| |

| |

Arithmetic Series | |

| |

| |

| |

Geometric Sequences and Series | |

| |

| |

Geometric Sequences | |

| |

| |

Geometric Series | |

| |

| |

Infinite Geometric Series | |

| |

| |

Annuities | |

| |

| |

Reviewing Basic Concepts (Sections 8.1-8.3) | |

| |

| |

| |

The Binomial Theorem | |

| |

| |

A Binomial Expansion Pattern | |

| |

| |

Pascal's Triangle | |

| |

| |

n-Factorial | |

| |

| |

Binomial Coefficients | |

| |

| |

The Binomial Theorem | |

| |

| |

rth Term of a Binomial Expansion | |

| |

| |

| |

Mathematical Induction | |

| |

| |

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) | |

| |

| |

| |

Counting Theory | |

| |

| |

Fundamental Principle of Counting | |

| |

| |

Permutations | |

| |

| |

Combinations | |

| |

| |

Distinguishing between Permutations and Combinations | |

| |

| |

| |

Probability | |

| |

| |

Basic Concepts | |

| |

| |

Complements and Venn Diagrams | |

| |

| |

Odds | |

| |

| |

Union of Two Events | |

| |

| |

Binomial Probability | |

| |

| |

Reviewing Basic Concepts (Sections 8.6 and 8.7) | |

| |

| |

Chapter 8 Summary | |

| |

| |

Chapter 8 Review Exercises | |

| |

| |

Chapter 8 Test | |

| |

| |

Chapter 8 Project Using Experimental Probabilities to Simulate Family Makeup | |

| |

| |

| |

Reference: Basic Algebraic Concepts | |

| |

| |

| |

Review of Exponents and Polynomials | |

| |

| |

Rules for Exponents | |

| |

| |

Terminology for Polynomials | |

| |

| |

Adding and Subtracting Polynomials | |

| |

| |

Multiplying Polynomials | |

| |

| |

| |

Review of Factoring | |

| |

| |

Factoring Out the Greatest Common Factor | |

| |

| |

Factoring by Grouping | |

| |

| |

Factoring Trinomials | |

| |

| |

Factoring Special Products | |

| |

| |

Factoring by Substitution | |

| |

| |

| |

Review of Rational Expressions | |

| |

| |

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 | |

| |

| |

Negative Exponents and the Quotient Rule | |

| |

| |

Rational Exponents | |

| |

| |

| |

Review of Radicals | |

| |

| |

Radical Notation | |

| |

| |

Rules for Radicals | |

| |

| |

Simplifying Radicals | |

| |

| |

Operations with Radicals | |

| |

| |

Rationalizing Denominators | |

| |

| |

Chapter R Test | |

| |

| |

| |

Geometry Formulas | |

| |

| |

| |

Deciding Which Model Best Fits a Set of Data | |

| |

| |

Answers to Selected Exercises | |

| |

| |

Index of Applications | |

| |

| |

Index | |