| |

| |

Introduction | |

| |

| |

Why You Need This Book | |

| |

| |

How to Use This Book | |

| |

| |

Visit Our Web Site | |

| |

| |

| |

Precalculus Prerequisites | |

| |

| |

Classifying Numbers | |

| |

| |

Interval Notation | |

| |

| |

Bounded intervals | |

| |

| |

Unbounded intervals | |

| |

| |

Algebraic Properties | |

| |

| |

The associative property | |

| |

| |

The commutative property | |

| |

| |

The distributive property | |

| |

| |

Identity elements | |

| |

| |

Inverse properties | |

| |

| |

Exponential Expressions | |

| |

| |

Radical Expressions | |

| |

| |

Properties of radicals | |

| |

| |

Simplifying radicals | |

| |

| |

Operations with radicals | |

| |

| |

Rationalizing expressions | |

| |

| |

Polynomial Expressions | |

| |

| |

Classifying polynomials | |

| |

| |

Adding and subtracting polynomials | |

| |

| |

Multiplying polynomials | |

| |

| |

Rational Expressions | |

| |

| |

Adding and subtracting rational expressions | |

| |

| |

Multiplying rational expressions | |

| |

| |

Simplifying complex fractions | |

| |

| |

Equations and Inequalities | |

| |

| |

Solving equations | |

| |

| |

Solving linear inequalities | |

| |

| |

Solving absolute value inequalities | |

| |

| |

Special inequality cases | |

| |

| |

Finding Linear Equations | |

| |

| |

| |

Functions | |

| |

| |

Relations vs. Functions | |

| |

| |

Understanding relations | |

| |

| |

Defining functions | |

| |

| |

Writing functions | |

| |

| |

Function Graphs | |

| |

| |

The vertical line test | |

| |

| |

Finding symmetry | |

| |

| |

Calculating intercepts | |

| |

| |

Determining domain and range | |

| |

| |

Eight Key Function Graphs | |

| |

| |

Basic Function Transformations | |

| |

| |

Vertical and horizontal shifts | |

| |

| |

Reflections | |

| |

| |

Stretching and squishing | |

| |

| |

Multiple transformations | |

| |

| |

Combining and Composing Functions | |

| |

| |

Arithmetic combinations | |

| |

| |

The composition of functions | |

| |

| |

Inverse Functions | |

| |

| |

What is an inverse function? | |

| |

| |

Graphs of inverse functions | |

| |

| |

Finding inverse functions | |

| |

| |

| |

Polynomial and Rational Functions | |

| |

| |

Factoring Polynomials | |

| |

| |

Greatest common factors | |

| |

| |

Factoring by grouping | |

| |

| |

Factoring quadratic trinomials | |

| |

| |

Special factor patterns | |

| |

| |

Solving Quadratic Equations | |

| |

| |

Factoring | |

| |

| |

The quadratic formula | |

| |

| |

Completing the square | |

| |

| |

Polynomial Division | |

| |

| |

Long division | |

| |

| |

Synthetic division | |

| |

| |

Important Root-Finding Theorems | |

| |

| |

The remainder theorem | |

| |

| |

The factor theorem | |

| |

| |

Calculating Roots | |

| |

| |

The Fundamental Theorem of Algebra | |

| |

| |

Descartes' Rule of Signs | |

| |

| |

The Rational Root Test | |

| |

| |

Determining roots | |

| |

| |

Advanced Graphing Techniques | |

| |

| |

The Leading Coefficient Test | |

| |

| |

Finding rational asymptotes | |

| |

| |

| |

Exponential and Logarithmic Functions | |

| |

| |

Exponential Functions | |

| |

| |

Natural exponential function | |

| |

| |

Graphs of exponential functions | |

| |

| |

Logarithmic Functions | |

| |

| |

Natural and common logs | |

| |

| |

Inverse relationship | |

| |

| |

Graphs of logarithmic functions | |

| |

| |

Change of base formula | |

| |

| |

Properties of Logarithms | |

| |

| |

Solving Exponential and Logarithmic Equations | |

| |

| |

Exponential equations | |

| |

| |

Logarithmic equations | |

| |

| |

Exponential Word Problems | |

| |

| |

Compound interest | |

| |

| |

Growth and decay | |

| |

| |

| |

Trigonometry | |

| |

| |

Measuring Angles | |

| |

| |

Characteristics of angles | |

| |

| |

Degrees and radians | |

| |

| |

Angle pairs | |

| |

| |

Coterminal angles | |

| |

| |

The Unit Circle | |

| |

| |

Right Triangle Trigonometry | |

| |

| |

Oblique Triangle Trigonometry | |

| |

| |

Reference angles | |

| |

| |

Calculating trigonometric ratios | |

| |

| |

Graphs of Sine and Cosine | |

| |

| |

Periodic graphs | |

| |

| |

Transforming sine and cosine | |

| |

| |

Other Trigonometric Function Graphs | |

| |

| |

Inverse Trigonometric Functions | |

| |

| |

| |

Analytic Trigonometry | |

| |

| |

Trigonometric Identities | |

| |

| |

Four types of identities | |

| |

| |

Simplifying expressions with identities | |

| |

| |

Proving Trigonometric Identities | |

| |

| |

Solving Trigonometric Equations | |

| |

| |

Simple equations | |

| |

| |

Quadratic equations | |

| |

| |

Equations requiring identities | |

| |

| |

Equations requiring squaring | |

| |

| |

Functions of multiple angles | |

| |

| |

Sum and Difference Identities | |

| |

| |

Additional Identities | |

| |

| |

Double-angle formulas | |

| |

| |

Half-angle formulas | |

| |

| |

Sum-product formulas | |

| |

| |

Product-sum formulas | |

| |

| |

Oblique Triangle Laws | |

| |

| |

Law of Sines | |

| |

| |

Law of Cosines | |

| |

| |

Calculating Triangle Area | |

| |

| |

Given Side-Angle-Side | |

| |

| |

Given side-side-side | |

| |

| |

| |

Vectors and the Trigonometry of Complex Numbers | |

| |

| |

Vectors in the Coordinate Plane | |

| |

| |

Standard form of a vector | |

| |

| |

Unit vectors | |

| |

| |

Basic vector operations | |

| |

| |

Dot Products | |

| |

| |

Properties of the dot product | |

| |

| |

Measuring angles between vectors | |

| |

| |

Orthogonal vectors | |

| |

| |

Complex Numbers and Trigonometry | |

| |

| |

Basic operations with complex numbers | |

| |

| |

Trigonometric form of a complex number | |

| |

| |

Multiplying and dividing complex numbers | |

| |

| |

Roots and Powers of Complex Numbers | |

| |

| |

DeMoivre's Theorem | |

| |

| |

Calculating nth roots of complex numbers | |

| |

| |

| |

Analytic Geometry | |

| |

| |

Conic Sections | |

| |

| |

Circles | |

| |

| |

Parabolas | |

| |

| |

Ellipses | |

| |

| |

Standard form | |

| |

| |

Eccentricity | |

| |

| |

Hyperbolas | |

| |

| |

Standard form | |

| |

| |

Graphing hyperbolas | |

| |

| |

Equations of asymptote lines | |

| |

| |

Identifying Conic Sections | |

| |

| |

Parametric Equations | |

| |

| |

Graphing parametric equations | |

| |

| |

Rewriting parametric equations | |

| |

| |

Polar Coordinates | |

| |

| |

Converting between polar and rectangular coordinates | |

| |

| |

Converting between polar and rectangular equations | |

| |

| |

| |

Matrices and Systems of Equations | |

| |

| |

Systems of Equations | |

| |

| |

Two-Variable Linear Systems | |

| |

| |

Substitution method | |

| |

| |

Elimination method | |

| |

| |

Nonlinear Systems of Equations | |

| |

| |

Characteristics of Matrices | |

| |

| |

Basic Matrix Operations | |

| |

| |

Adding matrices | |

| |

| |

Scalar multiplication | |

| |

| |

Subtracting matrices | |

| |

| |

Multiplying matrices | |

| |

| |

Solving Systems of Equations with Matrices | |

| |

| |

Gaussian and Gauss-Jordan elimination | |

| |

| |

Matrix row operations | |

| |

| |

Systems with infinitely many solutions | |

| |

| |

Inverse Matrices | |

| |

| |

Calculating inverse matrices | |

| |

| |

Solving matrix equations | |

| |

| |

Determinants | |

| |

| |

Determinants of 2 x 2 matrices | |

| |

| |

Minors and cofactors | |

| |

| |

Determinants of square matrices | |

| |

| |

Cramer's Rule | |

| |

| |

Graphs of Two-Variable Inequalities | |

| |

| |

Single inequalities | |

| |

| |

Systems of inequalities | |

| |

| |

Linear Programming | |

| |

| |

| |

Additional Topics | |

| |

| |

Binomial Expansion | |

| |

| |

Pascal's Triangle | |

| |

| |

Factorials | |

| |

| |

The Binomial Theorem | |

| |

| |

Ordered Number Lists | |

| |

| |

Sequences | |

| |

| |

Series | |

| |

| |

CQR Resource Center | |

| |

| |

Glossary for CQR Precalculus | |

| |

| |

Index | |