Chapter 1 Functions and Their Graphs

Section 1.1 Rectangular Coordinates
• Using the Rectangular Coordinate System
• Transformations of Graphs and Functions
• Plane Geometric Figures
• Volume
• Area


Section 1.2 Graphs of Equations
• Graphing Linear Equations of the Form Ax + By = C
• Graphs and Symmetry
• Circles
• Displaying Data in the Coordinate Plane


Section 1.3 Linear Equations in Two Variables
• Slope of a Line
• Writing Equations of Lines
• Writing Equations of Lines Given Two or More Points
• Parallel and Perpendicular Lines
• Displaying Data in the Coordinate Plane


Section 1.4 Functions
• Introduction to Functions
• Finding the Domain of a Rational Expression
• Identifying a Composition of Functions and Finding a Difference Quotient


Section 1.5 Analyzing Graphs of Functions
• Using Graphs and Functions
• Advanced Techniques for Graphing Polynomial Functions
• Zeros of Functions
• Graphs of Functions
• Displaying Data in the Coordinate Plane


Section 1.6 A Library of Parent Functions
• Writing Equations of Lines


Section 1.7 Transformations of Functions
• Transformations of Graphs and Functions
• Nonrigid Transformations of Graphs


Section 1.8 Combinations of Functions: Composite Functions
• Algebra of Functions


Section 1.9 Inverse Functions
• Inverse Functions
• Graphs and Inverse Functions


Section 1.10 Mathematical Modeling and Variation
• Linear Modeling with Least Squares Regression
• Variation

Chapter 2 Polynomial and Rational Functions

Section 2.1 Quadratic Functions and Models
• Graphs of Quadratic Functions
• Transformations of Graphs and Functions
• Finding the Maximum or Minimum Value of a Quadratic Function


Section 2.2 Polynomial Functions of Higher Degree
• Advanced Techniques for Graphing Polynomial Functions
• Finding Zeros of Polynomial Functions


Section 2.3 Polynomial and Synthetic Division
• Dividing Polynomials
• Synthetic Division


Section 2.4 Complex Numbers
• Introduction to Complex Numbers
• Operations with Complex Numbers
• Solving Quadratic Equations by Factoring and by Taking Square Roots


Section 2.5 Zeros of Polynomial Functions
• The Fundamental Theorem of Algebra
• Finding Zeros of Polynomial Functions


Section 2.6 Rational Functions
• The Domain and Slant Asymptotes of a Rational Function
• Graphs of Rational Functions


Section 2.7 Nonlinear Inequalities
• Quadratic, Rational, and Polynomial Inequalities

Chapter 3 Exponential and Logarithmic Functions

Section 3.1 Exponential Functions and Their Graphs
• Exponential Functions


Section 3.2 Logarithmic Functions and Their Graphs
• Introduction to Logarithms
• Graphs and Properties of Logarithms


Section 3.4 Exponential and Logarithmic Equations
• Exponential and Logarithmic Equations


Section 3.5 Exponential and Logarithmic Models
• Exponential Growth and Decay Problems
• Exponential and Logarithmic Models

Chapter 4 Trigonometry

Section 4.1 Radian and Degree Measure
• Angles Measured in Radians or Degrees
• Arcs, Arc Length, Linear Speed, and Angular Speed


Section 4.2 Trigonometric Functions: The Unit Circle
• Defining the Trigonometric Functions Using the Unit Circle


Section 4.3 Right Triangle Trigonometry
• Right Triangle Trigonometry
• Fundamental Trigonometric Identities


Section 4.4 Trigonometric Functions of Any Angle
• Trigonometric Functions of Any Angle


Section 4.5 Graphs of Sine and Cosine Functions
• Graphing Sine and Cosine Functions
• Finding a Trigonometric Model for Data


Section 4.6 Graphs of Other Trigonometric Functions
• Graphing Tangent and Cotangent Functions
• Graphs of the Reciprocal Functions
• Graphing Combinations of Trigonometric Functions


Section 4.7 Inverse Trigonometric Functions
• Inverse Trigonometric Functions


Section 4.8 Applications and Models
• Right Triangle Trigonometry
• Applications: Directional Bearings and Harmonic Motion

Chapter 5 Analytic Trigonometry

Section 5.1 Using Fundamental Identities
• Fundamental Trigonometric Identities


Section 5.2 Verifying Trigonometric Identities
• More Fundamental Trigonometric Identities


Section 5.3 Solving Trigonometric Equations
• Solving Trigonometric Equations


Section 5.4 Sum and Difference Formulas
• Using Sum and Difference Formulas


Section 5.5 Multiple-Angle and Product-to-Sum Formulas
• Multiple Angle Formulas
• Product-to-Sum and Sum-to-Product Formulas

Chapter 6 Additional Topics in Trigonometry

Section 6.1 Law of Sines
• Law of Sines


Section 6.2 Law of Cosines
• Law of Cosines


Section 6.3 Vectors in the Plane
• Vectors in the Plane
• Using Unit Vectors


Section 6.4 Vectors and Dot Products
• Vector Dot Products
• Finding Vector Components


Section 6.5 Trigonometric Form of a Complex Number
• Trigonometric Form of a Complex Number
• Powers and Roots of Complex Numbers: DeMoivre's Theorem

Chapter 7 Systems of Equations and Inequalities

Section 7.1 Linear and Nonlinear Systems of Equations
• Solving Systems of Linear Equations in Two Variables
• Solving Nonlinear Systems of Equations


Section 7.2 Two-Variable Linear Systems
• Systems of Linear Equations in Two Variables


Section 7.3 Multivariable Linear Systems
• Solving a System of Linear Equations in 3 Variables by Back-Substitution
• Solving Systems of Linear Equations in Three Variables


Section 7.4 Partial Fractions
• Partial Fractions


Section 7.5 Systems of Inequalities
• Nonlinear Inequalities and Systems of Inequalities

Chapter 8 Matrices and Determinants

Section 8.1 Matrices and Systems of Equations
• Matrices
Section 8.2 Operations with Matrices
• Equality of Matrices
• Matrix Operations
• Matrix Equations and Systems of Linear Equations


Section 8.3 The Inverse of a Square Matrix
• The Inverse of a Square Matrix


Section 8.4 The Determinant of a Square Matrix
• Determinants


Section 8.5 Applications of Matrices and Determinants
• Cramer's Rule

Chapter 9 Sequences, Series, and Probability

Section 9.1 Sequences and Series
• Introduction to Sequences and Series
• Recursive Sequences and Properties of Sums
• Introduction to Sequences and Series


Section 9.2 Arithmetic Sequences and Partial Sums
• Arithmetic Sequences and Series


Section 9.3 Geometric Sequences and Series
• Geometric Sequences and Series


Section 9.4 Mathematical Induction
• Mathematical Induction
• Sums of Powers of Integers and Finite Differences


Section 9.5 The Binomial Theorem
• Binomial Expansions


Section 9.6 Counting Principles
• Counting Principles
• Counting Techniques


Section 9.7 Probability
• Probability
• Probability of Compound Events

Chapter 10 Topics in Analytic Geometry

Section 10.1 Lines
• Lines in Analytic Geometry


Section 10.2 Introduction to Conics: Parabolas
• General Equations of Conics
• Parabolas
• Reflective Property of a Parabola


Section 10.3 Ellipses
• Ellipses and Hyperbolas Centered at (h, k)
• Eccentricity of Ellipses and Hyperbolas


Section 10.4 Hyperbolas
• Asymptotes of a Hyperbola
• General Equations of Conics


Section 10.5 Rotation of Conics
• Rotation of Axes


Section 10.6 Parametric Equations
• Parametric Equations


Section 10.7 Polar Coordinates
• Polar Coordinates


Section 10.8 Graphs of Polar Equations
• Graphs of Polar Equations


Section 10.9 Polar Equations of Conics
• Polar Equations of Conics

Chapter 11 Analytic Geometry in Three Dimensions

Section 11.1 The Three-Dimensional Coordinate System
• The 3-Dimensional Coordinate System
• Spheres


Section 11.2 Vectors in Space
• Vectors in Space


Section 11.3 The Cross Product of Two Vectors
• Cross Product of 2 Vectors


Section 11.4 Lines and Planes in Space
• Lines and Planes in Space

Chapter 12 Limits and an Introduction to Calculus

Section 12.1 Introduction to Limits
• Introduction to Limits


Section 12.2 Techniques for Evaluating Limits
• Techniques for Evaluating Limits


Section 12.3 The Tangent Line Problem
• The Tangent Line Problem


Section 12.4 Limits at Infinity and Limits of Sequences
• Evaluating a Limit at Infinity


Section 12.5 The Area Problem
• Factoring Special Products

Appendix A Review of Fundamental Concepts of Algebra

Section A.1 Real Numbers and Their Properties
• Introduction to Real Numbers
• Opposites and Absolute Value


Section A.2 Exponents and Radicals
• Exponents
• Exponents and Scientific Notation
• Rational Exponents and Radicals
• Expressions Involving nth-Root Radicals


Section A.3 Polynomials and Factoring
• Introduction to Polynomials
• Adding and Subtracting Polynomials
• Common Factors and Grouping
• Factoring Second Degree Trinomials


Section A.4 Rational Expressions
• Rational Expressions and Equations
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions


Section A.5 Solving Equations
• Solving Equations in One Variable
• Literal Equations and Equations with Fractions and Decimals
• Solving Equations by Factoring
• Solving Quadratic Equations by Factoring and by Taking Square Roots
• Solving Quadratic Equations by Completing the Square
• Solving Quadratic Equations Using the Quadratic Formula
• Equations with Radicals
• Literal Equations and Equations with Fractions and Decimals


Section A.6 Linear Inequalities in One Variable
• Inequalities in One Variable
• Absolute Value Equations and Inequalities


Section A.7 Errors and the Algebra of Calculus
• Simplifying Radical Expressions
• Exponents and Scientific Notation