Preface
Chapter 1  Prerequisites
Introduction to Prerequisites
1.1 Real Numbers: Algebra Essentials
1.2 Exponents and Scientific Notation
1.3 Radicals and Rational Exponents
1.4 Polynomials
1.5 Factoring Polynomials
1.6 Rational Expressions
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 2  Equations and Inequalities
Introduction to Equations and Inequalities
2.1 The Rectangular Coordinate Systems and Graphs
2.2 Linear Equations in One Variable
2.3 Models and Applications
2.4 Complex Numbers
2.5 Quadratic Equations
2.6 Other Types of Equations
2.7 Linear Inequalities and Absolute Value Inequalities
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 3  Functions
Introduction to Functions
3.1 Functions and Function Notation
3.2 Domain and Range
3.3 Rates of Change and Behavior of Graphs
3.4 Composition of Functions
3.5 Transformation of Functions
3.6 Absolute Value Functions
3.7 Inverse Functions
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 4  Linear Functions
Introduction to Linear Functions
4.1 Linear Functions
4.2 Modeling with Linear Functions
4.3 Fitting Linear Models to Data
Chapter Review
Key Terms
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 5  Polynomial and Rational Functions
Introduction to Polynomial and Rational Functions
5.1 Quadratic Functions
5.2 Power Functions and Polynomial Functions
5.3 Graphs of Polynomial Functions
5.4 Dividing Polynomials
5.5 Zeros of Polynomial Functions
5.6 Rational Functions
5.7 Inverses and Radical Functions
5.8 Modeling Using Variation
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 6  Exponential and Logarithmic Functions
Introduction to Exponential and Logarithmic Functions
6.1 Exponential Functions
6.2 Graphs of Exponential Functions
6.3 Logarithmic Functions
6.4 Graphs of Logarithmic Functions
6.5 Logarithmic Properties
6.6 Exponential and Logarithmic Equations
6.7 Exponential and Logarithmic Models
6.8 Fitting Exponential Models to Data
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 7  The Unit Circle: Sine and Cosine Functions
Introduction to The Unit Circle: Sine and Cosine Functions
7.1 Angles
7.2 Right Triangle Trigonometry
7.3 Unit Circle
7.4 The Other Trigonometric Functions
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 8  Periodic Functions
Introduction to Periodic Functions
8.1 Graphs of the Sine and Cosine Functions
8.2 Graphs of the Other Trigonometric Functions
8.3 Inverse Trigonometric Functions
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 9  Trigonometric Identities and Equations
Introduction to Trigonometric Identities and Equations
9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
9.2 Sum and Difference Identities
9.3 Double-Angle, Half-Angle, and Reduction Formulas
9.4 Sum-to-Product and Product-to-Sum Formulas
9.5 Solving Trigonometric Equations
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 10  Further Applications of Trigonometry
Introduction to Further Applications of Trigonometry
10.1 Non-right Triangles: Law of Sines
10.2 Non-right Triangles: Law of Cosines
10.3 Polar Coordinates
10.4 Polar Coordinates: Graphs
10.5 Polar Form of Complex Numbers
10.6 Parametric Equations
10.7 Parametric Equations: Graphs
10.8 Vectors
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 11  Systems of Equations and Inequalities
Introduction to Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Two Variables
11.2 Systems of Linear Equations: Three Variables
11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
11.4 Partial Fractions
11.5 Matrices and Matrix Operations
11.6 Solving Systems with Gaussian Elimination
11.7 Solving Systems with Inverses
11.8 Solving Systems with Cramer's Rule
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 12  Analytic Geometry
Introduction to Analytic Geometry
12.1 The Ellipse
12.2 The Hyperbola
12.3 The Parabola
12.4 Rotation of Axes
12.5 Conic Sections in Polar Coordinates
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Chapter 13  Sequences, Probability, and Counting Theory
Introduction to Sequences, Probability and Counting Theory
13.1 Sequences and Their Notations
13.2 Arithmetic Sequences
13.3 Geometric Sequences
13.4 Series and Their Notations
13.5 Counting Principles
13.6 Binomial Theorem
13.7 Probability
Chapter Review
Key Terms
Key Equations
Key Concepts
Exercises
Review Exercises
Practice Test
Appendix A Proofs, Identities, and Toolkit Functions
Answer Key
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Index