1. Linear Functions, Equations, and Inequalities

• 1.1 Real Numbers and the Rectangular Coordinate System
• 1.2 Introduction to Relations and Functions
• Reviewing Basic Concepts (Sections 1.1–1.2)
• 1.3 Linear Functions
• 1.4 Equations of Lines and Linear Models
• Reviewing Basic Concepts (Sections 1.3–1.4)
• 1.5 Linear Equations and Inequalities
• Unifying Linear Functions
• 1.6 Applications of Linear Functions
• Reviewing Basic Concepts (Sections 1.5–1.6)
• Summary
• Review Exercises
• Test

2. Analysis of Graphs of Functions

• 2.1 Graphs of Basic Functions and Relations; Symmetry
• 2.2 Vertical and Horizontal Shifts of Graphs
• 2.3 Stretching, Shrinking, and Reflecting Graphs
• Reviewing Basic Concepts (Sections 2.1–2.3)
• 2.4 Absolute Value Functions
• Unifying Absolute Value Functions
• 2.5 Piecewise-Defined Functions
• 2.6 Operations and Composition
• Reviewing Basic Concepts (Sections 2.4–2.6)
• Summary
• Review Exercises
• Test

• 3.1 Complex Numbers
• 3.2 Quadratic Functions and Graphs
• Reviewing Basic Concepts (Sections 3.1–3.2)
• 3.3 Quadratic Equations and Inequalities
• 3.4 Applications of Quadratic Functions and Models
• Reviewing Basic Concepts (Sections 3.3–3.4)
• Summary
• Review Exercises
• Test

4. Polynomial Functions of Higher Degree

• 4.1 Graphs of Polynomial Functions
• 4.2 Topics in the Theory of Polynomial Functions (I)
• Reviewing Basic Concepts (Sections 4.1–4.2)
• 4.3 Topics in the Theory of Polynomial Functions (II)
• 4.4 Polynomial Equations, Inequalities, Applications, and Models
• Reviewing Basic Concepts (Sections 4.3–4.4)
• Unifying Polynomial Functions
• Summary
• Review Exercises
• Test

5. Rational, Power, and Root Functions

• 5.1 Rational Functions and Graphs (I)
• 5.2 Rational Functions and Graphs (II)
• 5.3 Rational Equations, Inequalities, Models, and Applications
• Reviewing Basic Concepts (Sections 5.1–5.3)
• 5.4 Functions Defined by Powers and Roots
• 5.5 Equations, Inequalities, and Applications Involving Root Functions
• Reviewing Basic Concepts (Sections 5.4–5.5)
• Unifying Root Functions
• Summary
• Review Exercises
• Test

6. Inverse, Exponential, and Logarithmic Functions

• 6.1 Inverse Functions
• 6.2 Exponential Functions
• Unifying Exponential Functions
• 6.3 Logarithms and Their Properties
• Reviewing Basic Concepts (Sections 6.1­–6.3)
• 6.4 Logarithmic Functions
• 6.5 Exponential and Logarithmic Equations and Inequalities
• Unifying Logarithmic Functions
• 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions
• Reviewing Basic Concepts (Sections 6.4–6.6)
• Summary Exercises on Functions: Domains, Defining Equations, and Composition
• Summary
• Review Exercises
• Test

7. Systems and Matrices

• 7.1 Systems of Equations
• 7.2 Solution of Linear Systems in Three Variables
• 7.3 Solution of Linear Systems by Row Transformations
• Reviewing Basic Concepts (Sections 7.1–7.3)
• 7.4 Matrix Properties and Operations
• 7.5 Determinants and Cramer’s Rule
• 7.6 Solution of Linear Systems by Matrix Inverses
• Reviewing Basic Concepts (Sections 7.4–7.6)
• 7.7 Systems of Inequalities and Linear Programming
• 7.8 Partial Fractions
• Reviewing Basic Concepts (Sections 7.7–7.8)
• Summary
• Review Exercises
• Test

8. Conic Sections, Nonlinear Systems, and Parametric Equations

• 8.1 Circles Revisited and Parabolas
• 8.2 Ellipses and Hyperbolas
• Reviewing Basic Concepts (Sections 8.1–8.2)
• 8.3 The Conic Sections and Nonlinear Systems
• 8.4 Introduction to Parametric Equations
• Reviewing Basic Concepts (Sections 8.3–8.4)
• Summary
• Review Exercises
• Test

9. The Unit Circle and the Functions of Trigonometry

• 9.1 Angles, Arcs, and Their Measures
• 9.2 The Unit Circle and Its Functions
• 9.3 Graphs of the Sine and Cosine Functions
• 9.4 Graphs of the Other Circular Functions
• 9.5 Functions of Angles and Fundamental Angles
• 9.6 Evaluating Trigonometric Functions
• 9.7 Applications of Right Triangles
• 9.8 Harmonic Motion
• Summary
• Review Exercises
• Test

10. Trigonometric Identities and Equations

• 10.1 Trigonometric Identities
• 10.2 Sum and Difference Identities
• 10.3 Further Identities
• 10.4 The Inverse Circular Functions
• 10.5 Trigonometric Equations and Inequalities (I)
• 10.6 Trigonometric Equations and Inequalities (II)
• Unifying Trigonometric Functions
• Summary
• Review Exercises
• Test

11. Applications of Trigonometry and Vectors

• 11.1 The Law of Sines
• 11.2 The Law of Cosines and Area Formulas
• 11.3 Vectors and Their Applications
• 11.4 Trigonometric (Polar) Form of Complex Numbers
• 11.5 Powers and Roots of Complex Numbers
• 11.6 Polar Equations and Graphs
• 11.7 More Parametric Equations
• Summary
• Review Exercises
• Test

12. Further Topics in Algebra

• 12.1 Sequences and Series
• 12.2 Arithmetic Sequences and Series
• 12.3 Geometric Sequences and Series
• Reviewing Basic Concepts (Sections 9.1–9.3)
• 12.4 Counting Theory
• 12.5 The Binomial Theorem
• Reviewing Basic Concepts (Sections 9.4–9.5)
• 12.6 Mathematical Induction
• 12.7 Probability
• Reviewing Basic Concepts (Sections 9.6–9.7)
• Summary
• Review Exercises
• Test

13. Limits, Derivatives, and Definite Integrals

• 13.1 An Introduction to Limits
• 13.2 Techniques for Calculating Limits
• 13.3 One-Sided Limits and Limits Involving Infinity
• 13.4 Tangent Lines and Derivatives
• 13.5 Area and the Definite Integral

R. Review: Basic Algebraic Concepts

• R.1 Review of Sets
• R.2 Review of Exponents and Polynomials
• R.3 Review of Factoring
• R.4 Review of Rational Expressions
• R.5 Review of Negative and Rational Exponents
• Test

Appendix A: Geometry Formulas
Appendix B: Vectors in Space
Appendix C: Polar Form of Conic Sections
Appendix D: Rotation of Axes