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| Introduction | |
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| Why You Need This Book | |
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| How to Use This Book | |
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| Visit Our Web Site | |
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| Precalculus Prerequisites | |
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| Classifying Numbers | |
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| Interval Notation | |
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| Bounded intervals | |
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| Unbounded intervals | |
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| Algebraic Properties | |
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| The associative property | |
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| The commutative property | |
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| The distributive property | |
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| Identity elements | |
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| Inverse properties | |
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| Exponential Expressions | |
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| Radical Expressions | |
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| Properties of radicals | |
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| Simplifying radicals | |
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| Operations with radicals | |
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| Rationalizing expressions | |
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| Polynomial Expressions | |
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| Classifying polynomials | |
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| Adding and subtracting polynomials | |
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| Multiplying polynomials | |
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| Rational Expressions | |
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| Adding and subtracting rational expressions | |
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| Multiplying rational expressions | |
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| Simplifying complex fractions | |
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| Equations and Inequalities | |
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| Solving equations | |
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| Solving linear inequalities | |
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| Solving absolute value inequalities | |
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| Special inequality cases | |
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| Finding Linear Equations | |
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| Functions | |
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| Relations vs. Functions | |
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| Understanding relations | |
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| Defining functions | |
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| Writing functions | |
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| Function Graphs | |
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| The vertical line test | |
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| Finding symmetry | |
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| Calculating intercepts | |
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| Determining domain and range | |
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| Eight Key Function Graphs | |
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| Basic Function Transformations | |
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| Vertical and horizontal shifts | |
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| Reflections | |
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| Stretching and squishing | |
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| Multiple transformations | |
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| Combining and Composing Functions | |
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| Arithmetic combinations | |
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| The composition of functions | |
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| Inverse Functions | |
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| What is an inverse function? | |
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| Graphs of inverse functions | |
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| Finding inverse functions | |
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| Polynomial and Rational Functions | |
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| Factoring Polynomials | |
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| Greatest common factors | |
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| Factoring by grouping | |
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| Factoring quadratic trinomials | |
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| Special factor patterns | |
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| Solving Quadratic Equations | |
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| Factoring | |
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| The quadratic formula | |
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| Completing the square | |
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| Polynomial Division | |
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| Long division | |
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| Synthetic division | |
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| Important Root-Finding Theorems | |
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| The remainder theorem | |
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| The factor theorem | |
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| Calculating Roots | |
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| The Fundamental Theorem of Algebra | |
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| Descartes' Rule of Signs | |
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| The Rational Root Test | |
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| Determining roots | |
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| Advanced Graphing Techniques | |
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| The Leading Coefficient Test | |
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| Finding rational asymptotes | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions | |
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| Natural exponential function | |
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| Graphs of exponential functions | |
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| Logarithmic Functions | |
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| Natural and common logs | |
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| Inverse relationship | |
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| Graphs of logarithmic functions | |
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| Change of base formula | |
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| Properties of Logarithms | |
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| Solving Exponential and Logarithmic Equations | |
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| Exponential equations | |
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| Logarithmic equations | |
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| Exponential Word Problems | |
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| Compound interest | |
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| Growth and decay | |
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| Trigonometry | |
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| Measuring Angles | |
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| Characteristics of angles | |
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| Degrees and radians | |
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| Angle pairs | |
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| Coterminal angles | |
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| The Unit Circle | |
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| Right Triangle Trigonometry | |
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| Oblique Triangle Trigonometry | |
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| Reference angles | |
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| Calculating trigonometric ratios | |
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| Graphs of Sine and Cosine | |
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| Periodic graphs | |
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| Transforming sine and cosine | |
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| Other Trigonometric Function Graphs | |
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| Inverse Trigonometric Functions | |
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| Analytic Trigonometry | |
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| Trigonometric Identities | |
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| Four types of identities | |
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| Simplifying expressions with identities | |
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| Proving Trigonometric Identities | |
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| Solving Trigonometric Equations | |
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| Simple equations | |
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| Quadratic equations | |
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| Equations requiring identities | |
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| Equations requiring squaring | |
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| Functions of multiple angles | |
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| Sum and Difference Identities | |
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| Additional Identities | |
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| Double-angle formulas | |
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| Half-angle formulas | |
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| Sum-product formulas | |
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| Product-sum formulas | |
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| Oblique Triangle Laws | |
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| Law of Sines | |
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| Law of Cosines | |
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| Calculating Triangle Area | |
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| Given Side-Angle-Side | |
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| Given side-side-side | |
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| Vectors and the Trigonometry of Complex Numbers | |
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| Vectors in the Coordinate Plane | |
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| Standard form of a vector | |
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| Unit vectors | |
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| Basic vector operations | |
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| Dot Products | |
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| Properties of the dot product | |
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| Measuring angles between vectors | |
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| Orthogonal vectors | |
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| Complex Numbers and Trigonometry | |
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| Basic operations with complex numbers | |
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| Trigonometric form of a complex number | |
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| Multiplying and dividing complex numbers | |
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| Roots and Powers of Complex Numbers | |
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| DeMoivre's Theorem | |
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| Calculating nth roots of complex numbers | |
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| Analytic Geometry | |
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| Conic Sections | |
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| Circles | |
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| Parabolas | |
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| Ellipses | |
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| Standard form | |
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| Eccentricity | |
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| Hyperbolas | |
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| Standard form | |
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| Graphing hyperbolas | |
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| Equations of asymptote lines | |
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| Identifying Conic Sections | |
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| Parametric Equations | |
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| Graphing parametric equations | |
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| Rewriting parametric equations | |
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| Polar Coordinates | |
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| Converting between polar and rectangular coordinates | |
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| Converting between polar and rectangular equations | |
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| Matrices and Systems of Equations | |
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| Systems of Equations | |
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| Two-Variable Linear Systems | |
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| Substitution method | |
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| Elimination method | |
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| Nonlinear Systems of Equations | |
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| Characteristics of Matrices | |
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| Basic Matrix Operations | |
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| Adding matrices | |
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| Scalar multiplication | |
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| Subtracting matrices | |
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| Multiplying matrices | |
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| Solving Systems of Equations with Matrices | |
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| Gaussian and Gauss-Jordan elimination | |
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| Matrix row operations | |
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| Systems with infinitely many solutions | |
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| Inverse Matrices | |
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| Calculating inverse matrices | |
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| Solving matrix equations | |
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| Determinants | |
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| Determinants of 2 x 2 matrices | |
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| Minors and cofactors | |
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| Determinants of square matrices | |
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| Cramer's Rule | |
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| Graphs of Two-Variable Inequalities | |
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| Single inequalities | |
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| Systems of inequalities | |
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| Linear Programming | |
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| Additional Topics | |
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| Binomial Expansion | |
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| Pascal's Triangle | |
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| Factorials | |
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| The Binomial Theorem | |
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| Ordered Number Lists | |
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| Sequences | |
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| Series | |
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| CQR Resource Center | |
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| Glossary for CQR Precalculus | |
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| Index | |