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| Preface | |
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| Linear Functions, Equations, and Inequalities | |
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| Real Numbers and the Rectangular Coordinate System | |
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| Sets of Real Numbers | |
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| The Rectangular Coordinate System | |
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| Viewing Windows | |
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| Roots | |
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| Distance and Midpoint Formulas | |
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| Introduction to Relations and Functions | |
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| Set-Builder Notation and Interval Notation | |
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| Relations, Domain, and Range | |
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| Functions | |
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| Tables | |
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| Function Notation | |
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| Reviewing Basic Concepts (Sections 1.1 and 1.2) | |
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| Linear Functions | |
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| Basic Concepts about Linear Functions | |
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| Slope of a Line | |
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| Slope-Intercept Form of the Equation of a Line | |
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| Equations of Lines and Linear Models | |
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| Point-Slope Form of the Equation of a Line | |
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| Standard Form of the Equation of a Line | |
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| Parallel and Perpendicular Lines | |
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| Linear Models and Regression | |
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| Reviewing Basic Concepts (Sections 1.3 and 1.4) | |
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| Linear Equations and Inequalities | |
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| Solving Linear Equations | |
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| Graphical Approaches to Solving Linear Equations | |
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| Identities and Contradictions | |
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| Solving Linear Inequalities | |
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| Graphical Approaches to Solving Linear Inequalities | |
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| Three-Part Inequalities | |
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| Applications of Linear Functions | |
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| Problem-Solving Strategies | |
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| Applications of Linear Equations | |
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| Break-Even Analysis | |
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| Direct Variation | |
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| Formulas | |
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| Reviewing Basic Concepts (Sections 1.5 and 1.6) | |
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| Chapter 1 Summary | |
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| Chapter 1 Review Exercises | |
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| Chapter 1 Test | |
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| Chapter 1 Project: Predicting Heights and Weights of Athletes | |
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| Analysis of Graphs of Functions | |
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| Graphs of Basic Functions and Relations; Symmetry | |
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| Continuity | |
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| Increasing and Decreasing Functions | |
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| The Identity Function | |
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| The Squaring Function and Symmetry with Respect to the y-Axis | |
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| The Cubing Function and Symmetry with Respect to the Origin | |
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| The Square Root and Cube Root Functions | |
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| The Absolute Value Function | |
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| The Relation x - y[superscript 2] and Symmetry with Respect to the x-Axis | |
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| Even and Odd Functions | |
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| Vertical and Horizontal Shifts of Graphs | |
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| Vertical Shifts | |
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| Horizontal Shifts | |
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| Combinations of Vertical and Horizontal Shifts | |
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| Effects of Shifts on Domain and Range | |
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| Horizontal Shifts Applied to Equations for Modeling | |
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| Stretching, Shrinking, and Reflecting Graphs | |
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| Vertical Stretching | |
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| Vertical Shrinking | |
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| Horizontal Stretching and Shrinking | |
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| Reflecting across an Axis | |
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| Combining Transformations of Graphs | |
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| Reviewing Basic Concepts (Sections 2.1-2.3) | |
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| Absolute Value Functions: Graphs, Equations, Inequalities, and Applications | |
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| The Graph of y = [vertical bar]f(x)[vertical bar] | |
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| Properties of Absolute Value | |
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| Equations and Inequalities Involving Absolute Value | |
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| An Application Involving Absolute Value | |
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| Piecewise-Defined Functions | |
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| Graphing Piecewise-Defined Functions | |
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| The Greatest Integer Function | |
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| Applications of Piecewise-Defined Functions | |
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| Operations and Composition | |
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| Operations on Functions | |
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| The Difference Quotient | |
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| Composition of Functions | |
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| Applications of Operations and Composition | |
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| Reviewing Basic Concepts (Sections 2.4-2.6) | |
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| Chapter 2 Summary | |
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| Chapter 2 Review Exercises | |
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| Chapter 2 Test | |
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| Chapter 2 Project: Modeling the Movement of a Cold Front | |
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| Polynomial Functions | |
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| Complex Numbers | |
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| The Number i | |
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| Operations with Complex Numbers | |
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| Quadratic Functions and Graphs | |
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| Completing the Square | |
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| Graphs of Quadratic Functions | |
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| Vertex Formula | |
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| Extreme Values | |
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| Applications and Quadratic Models | |
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| Quadratic Equations and Inequalities | |
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| Zero-Product Property | |
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| Solving x[superscript 2] = k | |
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| Quadratic Formula and the Discriminant | |
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| Solving Quadratic Equations | |
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| Solving Quadratic Inequalities | |
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| Formulas Involving Quadratics | |
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| Another Quadratic Model | |
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| Reviewing Basic Concepts (Sections 3.1-3.3) | |
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| Further Applications of Quadratic Functions and Models | |
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| Applications of Quadratic Functions | |
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| Quadratic Models | |
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| Higher-Degree Polynomial Functions and Graphs | |
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| Cubic Functions | |
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| Quartic Functions | |
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| Extrema | |
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| End Behavior | |
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| x-Intercepts (Real Zeros) | |
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| Comprehensive Graphs | |
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| Curve Fitting and Polynomial Models | |
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| Reviewing Basic Concepts (Sections 3.4 and 3.5) | |
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| Topics in the Theory of Polynomial Functions (I) | |
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| Intermediate Value Theorem | |
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| Division of Polynomials and Synthetic Division | |
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| Remainder and Factor Theorems | |
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| Topics in the Theory of Polynomial Functions (II) | |
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| Complex Zeros and the Fundamental Theorem of Algebra | |
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| Number of Zeros | |
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| Rational Zeros Theorem | |
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| Descartes' Rule of Signs | |
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| Boundedness Theorem | |
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| Polynomial Equations and Inequalities; Further Applications and Models | |
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| Polynomial Equations and Inequalities | |
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| Complex nth Roots | |
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| Applications and Polynomial Models | |
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| Reviewing Basic Concepts (Sections 3.6-3.8) | |
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| Chapter 3 Summary | |
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| Chapter 3 Review Exercises | |
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| Chapter 3 Test | |
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| Chapter 3 Project: Creating a Social Security Polynomial | |
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| Rational, Power, and Root Functions | |
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| Rational Functions and Graphs | |
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| The Reciprocal Function | |
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| The Rational Function Defined by f(x) = 1 / x[superscript 2] | |
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| More on Graphs of Rational Functions | |
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| Vertical and Horizontal Asymptotes | |
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| Graphing Techniques | |
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| Oblique Asymptotes | |
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| Graphs with Points of Discontinuity | |
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| Rational Equations, Inequalities, Applications, and Models | |
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| Solving Rational Equations and Inequalities | |
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| Applications and Models of Rational Functions | |
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| Inverse Variation | |
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| Combined and Joint Variation | |
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| Reviewing Basic Concepts (Sections 4.1-4.3) | |
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| Functions Defined by Powers and Roots | |
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| Power and Root Functions | |
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| Modeling Using Power Functions | |
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| Graphs of f(x) = [characters not reproducible] | |
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| Graphing Circles and Horizontal Parabolas Using Root Functions | |
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| Equations, Inequalities, and Applications Involving Root Functions | |
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| Equations and Inequalities | |
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| An Application of Root Functions | |
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| Reviewing Basic Concepts (Sections 4.4 and 4.5) | |
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| Chapter 4 Summary | |
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| Chapter 4 Review Exercises | |
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| Chapter 4 Test | |
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| Chapter 4 Project: How Rugged Is Your Coastline? | |
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| Inverse, Exponential, and Logarithmic Functions | |
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| Inverse Functions | |
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| Inverse Operations | |
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| One-to-One Functions | |
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| Inverse Functions and Their Graphs | |
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| Equations of Inverse Functions | |
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| An Application of Inverse Functions | |
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| Exponential Functions | |
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| Real-Number Exponents | |
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| Graphs of Exponential Functions | |
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| Exponential Equations (Type 1) | |
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| Compound Interest | |
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| The Number e and Continuous Compounding | |
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| An Application of Exponential Functions | |
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| Logarithms and Their Properties | |
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| Definition of Logarithm | |
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| Common Logarithms | |
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| Natural Logarithms | |
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| Properties of Logarithms | |
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| Change-of-Base Rule | |
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| Reviewing Basic Concepts (Sections 5.1-5.3) | |
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| Logarithmic Functions | |
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| Graphs of Logarithmic Functions | |
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| Applying Earlier Work to Logarithmic Functions | |
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| A Logarithmic Model | |
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| Exponential and Logarithmic Equations and Inequalities | |
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| Exponential Equations and Inequalities (Type 2) | |
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| Logarithmic Equations and Inequalities | |
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| Equations and Inequalities Involving Both Exponentials and Logarithms | |
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| Formulas Involving Exponentials and Logarithms | |
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| Reviewing Basic Concepts (Sections 5.4 and 5.5) | |
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| Further Applications and Modeling with Exponential and Logarithmic Functions | |
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| Physical Science Applications | |
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| Financial Applications | |
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| Biological and Medical Applications | |
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| Modeling Data with Exponential and Logarithmic Functions | |
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| Chapter 5 Summary | |
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| Chapter 5 Review Exercises | |
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| Chapter 5 Test | |
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| Chapter 5 Project: Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models) | |
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| Analytic Geometry | |
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| Circles and Parabolas | |
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| Conic Sections | |
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| Equations and Graphs of Circles | |
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| Equations and Graphs of Parabolas | |
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| Translations of Parabolas | |
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| An Application of Parabolas | |
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| Ellipses and Hyperbolas | |
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| Equations and Graphs of Ellipses | |
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| Translations of Ellipses | |
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| An Application of Ellipses | |
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| Equations and Graphs of Hyperbolas | |
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| Translations of Hyperbolas | |
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| Reviewing Basic Concepts (Sections 6.1 and 6.2) | |
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| Summary of the Conic Sections | |
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| Characteristics | |
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| Identifying Conic Sections | |
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| Eccentricity | |
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| Parametric Equations | |
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| Graphs of Parametric Equations and Their Rectangular Equivalents | |
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| Alternative Forms of Parametric Equations | |
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| An Application of Parametric Equations | |
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| Reviewing Basic Concepts (Sections 6.3 and 6.4) | |
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| Chapter 6 Summary | |
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| Chapter 6 Review Exercises | |
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| Chapter 6 Test | |
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| Chapter 6 Project: Modeling the Path of a Bouncing Ball | |
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| Systems of Equations and Inequalities; Matrices | |
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| Systems of Equations | |
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| Linear Systems | |
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| Substitution Method | |
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| Elimination Method | |
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| Special Systems | |
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| Nonlinear Systems | |
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| Applications of Systems | |
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| Solution of Linear Systems in Three Variables | |
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| Geometric Considerations | |
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| Analyttic Solution of Systems in Three Variables | |
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| Applications of Systems | |
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| Curve Fitting Using a System | |
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| Solution of Linear Systems by Row Transformations | |
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| Matrix Row Transformations | |
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| Row Echelon Method | |
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| Reduced Row Echelon Method | |
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| Special Cases | |
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| An Application of Matrices | |
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| Reviewing Basic Concepts (Sections 7.1-7.3) | |
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| Matrix Properties and Operations | |
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| Terminology of Matrices | |
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| Operations on Matrices | |
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| Applying Matrix Algebra | |
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| Determinants and Cramer's Rule | |
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| Determinants of 2 x 2 Matrices | |
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| Determinants of Larger Matrices | |
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| Derivation of Cramer's Rule | |
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| Using Cramer's Rule to Solve Systems | |
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| Solution of Linear Systems by Matrix Inverses | |
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| Identity Matrices | |
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| Multiplicative Inverses of Square Matrices | |
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| Using Determinants to Find Inverses | |
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| Solving Linear Systems Using Inverse Matrices | |
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| Curve Fitting Using a System | |
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| Reviewing Basic Concepts (Sections 7.4-7.6) | |
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| Systems of Inequalities and Linear Programming | |
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| Solving Linear Inequalities | |
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| Solving Systems of Inequalities | |
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| Linear Programming | |
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| Partial Fractions | |
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| Decomposition of Rational Expressions | |
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| Distinct Linear Factors | |
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| Repeated Linear Factors | |
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| Distinct Linear and Quadratic Factors | |
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| Repeated Quadratic Factors | |
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| Reviewing Basic Concepts (Sections 7.7 and 7.8) | |
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| Chapter 7 Summary | |
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| Chapter 7 Review Exercises | |
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| Chapter 7 Test | |
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| Chapter 7 Project: Finding a Polynomial Whose Graph Passes through Any Number of Given Points | |
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| Trigonometric Functions and Applications | |
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| Angles and Their Measures | |
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| Basic Terminology | |
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| Degree Measure | |
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| Standard Position and Coterminal Angles | |
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| Radian Measure | |
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| Arc Lengths and Areas of Sectors | |
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| Angular and Linear Speed | |
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| Trigonometric Functions and Fundamental Identities | |
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| Trigonometric Functions | |
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| Quadrantal Angles | |
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| Reciprocal Identities | |
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| Signs and Ranges of Function Values | |
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| Pythagorean Identities | |
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| Quotient Identities | |
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| An Application of Trigonometric Functions | |
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| Reviewing Basic Concepts (Sections 8.1 and 8.2) | |
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| Evaluating Trigonometric Functions | |
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| Definitions of the Trigonometric Functions | |
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| Trigonometric Function Values of Special Angles | |
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| Cofunction Identities | |
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| Reference Angles | |
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| Special Angles as Reference Angles | |
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| Finding Function Values with a Calculator | |
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| Finding Angle Measures | |
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| Applications of Right Triangles | |
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| Significant Digits | |
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| Solving Triangles | |
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| Angles of Elevation or Depression | |
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| Bearing | |
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| Further Applications of Trigonometric Functions | |
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| Reviewing Basic Concepts (Sections 8.3 and 8.4) | |
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| The Circular Functions | |
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| Circular Functions | |
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| Applications of Circular Functions | |
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| Graphs of the Sine and Cosine Functions | |
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| Periodic Functions | |
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| Graph of the Sine Function | |
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| Graph of the Cosine Function | |
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| Graphing Techniques, Amplitude, and Period | |
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| Translations | |
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| Determining a Trigonometric Model Using Curve Fitting | |
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| Reviewing Basic Concepts (Sections 8.5 and 8.6) | |
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| Graphs of the Other Circular Functions | |
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| Graphs of the Cosecant and Secant Functions | |
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| Graphs of the Tangent and Cotangent Functions | |
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| Addition of Ordinates | |
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| Harmonic Motion | |
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| Simple Harmonic Motion | |
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| Damped Oscillatory Motion | |
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| Reviewing Basic Concepts (Sections 8.7 and 8.8) | |
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| Chapter 8 Summary | |
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| Chapter 8 Review Exercises | |
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| Chapter 8 Test | |
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| Chapter 8 Project: Modeling Sunset Times | |
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| Trigonometric Identities and Equations | |
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| Trigonometric Identities | |
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| Fundamental Identities | |
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| Using the Fundamental Identities | |
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| Verifying Identities | |
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| Sum and Difference Identities | |
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| Cosine Sum and Difference Identities | |
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| Sine and Tangent Sum and Difference Identities | |
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| Reviewing Basic Concepts (Sections 9.1 and 9.2) | |
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| Further Identities | |
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| Double-Number Identities | |
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| Product-to-Sum and Sum-to-Product Identities | |
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| Half-Number Identities | |
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| The Inverse Circular Functions | |
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| Review of Inverse Functions | |
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| Inverse Sine Function | |
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| Inverse Cosine Function | |
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| Inverse Tangent Function | |
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| Remaining Inverse Trigonometric Functions | |
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| Inverse Function Values | |
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| Reviewing Basic Concepts (Sections 9.3 and 9.4) | |
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| Trigonometric Equations and Inequalities (I) | |
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| Equations Solvable by Linear Methods | |
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| Equations Solvable by Factoring | |
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| Equations Solvable by the Quadratic Formula | |
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| Using Trigonometric Identities to Solve Equations | |
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| Trigonometric Equations and Inequalities (II) | |
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| Equations and Inequalities Involving Multiple-Number Identities | |
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| Equations and Inequalities Involving Half-Number Identities | |
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| An Application of Trigonometric Equations | |
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| Reviewing Basic Concepts (Sections 9.5 and 9.6) | |
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| Chapter 9 Summary | |
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| Chapter 9 Review Exercises | |
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| Chapter 9 Test | |
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| Chapter 9 Project: Modeling a Damped Pendulum | |
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| Applications of Trigonometry; Vectors | |
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| The Law of Sines | |
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| Congruency and Oblique Triangles | |
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| Derivation of the Law of Sines | |
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| Applications of Triangles | |
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| Ambiguous Case | |
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| The Law of Cosines and Area Formulas | |
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| Derivation of the Law of Cosines | |
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| Applications of Triangles | |
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| Area Formulas | |
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| Vectors and Their Applications | |
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| Basic Terminology | |
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| Algebraic Interpretation of Vectors | |
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| Operations with Vectors | |
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| Dot Product and the Angle between Vectors | |
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| Applications of Vectors | |
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| Reviewing Basic Concepts (Sections 10.1-10.3) | |
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| Trigonometric (Polar) Form of Complex Numbers | |
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| The Complex Plane and Vector Representation | |
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| Trigonometric (Polar) Form | |
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| Products of Complex Numbers in Trigonometric Form | |
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| Quotients of Complex Numbers in Trigonometric Form | |
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| Powers and Roots of Complex Numbers | |
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| Powers of Complex Numbers (De Moivre's Theorem) | |
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| Roots of Complex Numbers | |
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| Reviewing Basic Concepts (Sections 10.4 and 10.5) | |
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| Polar Equations and Graphs | |
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| Polar Coordinate System | |
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| Graphs of Polar Equations | |
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| Classifying Polar Equations | |
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| Converting Equations | |
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| More Parametric Equations | |
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| Parametric Equations with Trigonometric Functions | |
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| The Cycloid | |
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| Applications of Parametric Equations | |
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| Reviewing Basic Concepts (Sections 10.6 and 10.7) | |
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| Chapter 10 Summary | |
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| Chapter 10 Review Exercises | |
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| Chapter 10 Test | |
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| Chapter 10 Project: When Is a Circle Really a Polygon? | |
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| Further Topics in Algebra | |
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| Sequences and Series | |
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| Sequences | |
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| Series and Summation Notation | |
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| Summation Properties | |
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| Arithmetic Sequences and Series | |
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| Arithmetic Sequences | |
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| Arithmetic Series | |
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| Geometric Sequences and Series | |
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| Geometric Sequences | |
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| Geometric Series | |
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| Infinite Geometric Series | |
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| Annuities | |
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| Reviewing Basic Concepts (Sections 11.1-11.3) | |
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| The Binomial Theorem | |
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| A Binomial Expansion Pattern | |
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| Pascal's Triangle | |
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| n-Factorial | |
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| Binomial Coefficients | |
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| The Binomial Theorem | |
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| rth Term of a Binomial Expansion | |
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| Mathematical Induction | |
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| Proof by Mathematical Induction | |
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| Proving Statements | |
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| Generalized Principle of Mathematical Induction | |
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| Proof of the Binomial Theorem | |
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| Reviewing Basic Concepts (Sections 11.4 and 11.5) | |
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| Counting Theory | |
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| Fundamental Principle of Counting | |
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| Permutations | |
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| Combinations | |
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| Distinguishing between Permutations and Combinations | |
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| Probability | |
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| Basic Concepts | |
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| Complements and Venn Diagrams | |
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| Odds | |
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| Union of Two Events | |
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| Binomial Probability | |
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| Reviewing Basic Concepts (Sections 11.6 and 11.7) | |
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| Chapter 11 Summary | |
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| Chapter 11 Review Exercises | |
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| Chapter 11 Test | |
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| Chapter 11 Project: Using Experimental Probabilities to Simulate Family Makeup | |
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| Reference: Basic Algebraic Concepts | |
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| Review of Exponents and Polynomials | |
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| Rules for Exponents | |
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| Terminology for Polynomials | |
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| Adding and Subtracting Polynomials | |
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| Multiplying Polynomials | |
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| Review of Factoring | |
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| Factoring Out the Greatest Common Factor | |
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| Factoring by Grouping | |
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| Factoring Trinomials | |
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| Factoring Special Products | |
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| Factoring by Substitution | |
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| Review of Rational Expressions | |
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| Domain of a Rational Expression | |
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| Lowest Terms of a Rational Expression | |
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| Multipling and Dividing Rational Expressions | |
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| Adding and Subtracting Rational Expressions | |
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| Complex Fractions | |
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| Review of Negative and Rational Exponents | |
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| Negative Exponents and the Quotient Rule | |
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| Rational Exponents | |
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| Review of Radicals | |
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| Radical Notation | |
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| Rules for Radicals | |
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| Simplifying Radicals | |
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| Operations with Radicals | |
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| Rationalizing Denominators | |
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| Chapter R Test | |
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| Geometry Formulas | |
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| Deciding Which Model Best Fits a Set of Data | |
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| Vectors in Space | |
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| Polar Form of Conic Sections | |
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| Rotation of Axes | |
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| Answers to Selected Exercises | |
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| Index of Applications | |
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| Index | |