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Preface | |

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Algebra: The Fundamentals | |

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The Real Numbers | |

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Different Perspectives: Inequalities | |

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Operations with Real Numbers | |

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Polynomials and Rational Expressions | |

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Exponents and Radicals | |

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The Complex Numbers | |

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First-Degree Equations and Inequalities in One Variable | |

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Absolute Value Equations and Inequalities | |

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Different Perspectives: Absolute Value Equations and Inequalities | |

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Quadratic Equations and Equations in Quadratic Form | |

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Quadratic and Rational Inequalities | |

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Substitution | |

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Review Exercises | |

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Practice Test | |

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Functions and Graphs: Part I | |

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The Cartesian Coordinate System: Graphing Straight Lines and Circles | |

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Different Perspectives: The Graph of an Equation | |

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Different Perspectives: Intercepts | |

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Slope | |

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Equations of a Line | |

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Technology Corner | |

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Relations and Functions | |

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Different Perspectives: Representing Relations | |

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Different Perspectives: Functions | |

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Function Notation | |

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Different Perspectives: Function Notation | |

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Relating Functions to Their Graphs | |

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Different Perspectives: Solving f(x) = k | |

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Different Perspectives: The Zeros of a Function | |

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Different Perspectives: Solving Inequalities | |

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Introduction to Graph Sketching: Symmetry | |

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Different Perspectives: Symmetry | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Functions and Graphs: Part II | |

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Basic Graphing Principles | |

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Different Perspectives: The Vertical Shift Principle | |

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Different Perspectives: The Horizontal Shift Principle | |

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Technology Corner | |

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More Graphing Principles: Types of Functions | |

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Extracting Functions from Real-Life Situations | |

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Quadratic Functions | |

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Operations on Functions | |

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Technology Corner | |

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Inverse Functions | |

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Different Perspectives: One-to-One Functions | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Polynomial, Rational, and Radical Functions | |

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Polynomial Functions | |

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Different Perspectives: End Behavior | |

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More on Polynomial Functions and Mathematical Models | |

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Polynomial Division, Roots of Polynomial Equations: The Remainder and Factor Theorems | |

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Roots of Polynomial Equations (continued): The Rational Root Theorem and Descartes' Rule of Signs | |

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Rational Functions | |

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Radical Functions | |

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Variation | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Exponential and Logarithmic Functions | |

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Exponential Functions | |

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Logarithmic Functions | |

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Properties of Logarithms; Logarithmic Equations | |

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Common and Natural Logarithms; Exponential Equations and Change of Base | |

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Applications | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Interim Review 1 (Chapters 1-5) | |

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Trigonometry | |

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Angle Measurement and Two Special Triangles | |

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Technology Corner | |

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The Trigonometric Functions | |

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Right-Triangle Trigonometry and Applications | |

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The Trigonometric Functions as Functions of Real Numbers | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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The Trigonometric Functions | |

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The Sine and Cosine Functions and Their Graphs | |

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The Tangent, Secant, Cosecant, and Cotangent Functions | |

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Basic Identities | |

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Trigonometric Equations | |

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Different Perspectives: Trigonometric Equations | |

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The Inverse Trigonometric Functions | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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More Trigonometry and Its Applications | |

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The Addition Formulas | |

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The Double-Angle and Half-Angle Formulas | |

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The Law of Sines and the Law of Cosines | |

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Vectors | |

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The Trigonometric Form of Complex Numbers and DeMoivre's Theorem | |

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Polar Coordinates | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Interim Review 2 (Chapters 6-8) | |

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Systems of Linear Equations and Inequalities | |

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2 x 2 Linear Systems: Elimination and Substitution | |

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3 x 3 Linear Systems: Elimination and Gaussian Elimination | |

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Solving Linear Systems Using Augmented Matrices | |

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The Algebra of Matrices | |

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Solving Linear Systems Using Matrix Inverses | |

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Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems | |

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Properties of Determinants | |

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Systems of Linear Inequalities | |

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An Introduction to Linear Programming: Geometric Solutions | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Conic Sections and Nonlinear Systems | |

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Conic Sections: Circles | |

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The Parabola | |

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The Ellipse | |

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Different Perspectives: Eccentricity | |

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The Hyperbola | |

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Identifying Conic Sections: Degenerate Forms | |

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Translations and Rotations of Coordinate Axes | |

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Nonlinear Systems of Equations and Inequalities | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Sequences, Series, and Related Topics | |

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Sequences | |

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Series and Sigma Notation | |

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Arithmetic Sequences and Series | |

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Geometric Sequences and Series | |

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Mathematical Induction | |

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Permutations and Combinations | |

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The Binomial Theorem | |

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Summary | |

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Review Exercises | |

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Practice Test | |

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Using Technology to Model Data | |

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Answers to Selected Exercises | |

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Index of Applications | |

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Index | |