Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, 5th edition

1. Functions and Their Graphs 

• 1.1 Functions 
• 1.2 The Graph of a Function 
• 1.3 Properties of Functions 
• 1.4 Library of Functions; Piecewise-defined Functions 
• 1.5 Graphing Techniques: Transformations 
• 1.6 Building Mathematical Models from Verbal Descriptions 
• 1.7 Building Mathematical Models Using Variation 
• Chapter Review 
• Chapter Test 
• Chapter Projects 

2. Linear and Quadratic Functions 

• 2.1 Properties of Linear Functions and Linear Models 
• 2.2 Building Linear Models from Data 
• 2.3 Quadratic Functions and Their Zeros 
• 2.4 Properties of Quadratic Functions 
• 2.5 Inequalities Involving Quadratic Functions 
• 2.6 Building Quadratic Models from Verbal Descriptions and from Data 
• 2.7 Complex Zeros of a Quadratic Function 
• 2.8 Equations and Inequalities Involving the Absolute Value Function 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

3. Polynomial and Rational Functions 

• 3.1 Polynomial Functions 
• 3.2 Graphing Polynomial Functions; Models 
• 3.3 The Real Zeros of a Polynomial Function 
• 3.4 Complex Zeros; Fundamental Theorem of Algebra 
• 3.5 Properties of Rational Functions 
• 3.6 The Graph of a Rational Function 
• 3.7 Polynomial and Rational Inequalities 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

4. Exponential and Logarithmic Functions 

• 4.1 Composite Functions 
• 4.2 One-to-One Functions; Inverse Functions 
• 4.3 Exponential Functions 
• 4.4 Logarithmic Functions 
• 4.5 Properties of Logarithms 
• 4.6 Logarithmic and Exponential Equations 
• 4.7 Financial Models 
• 4.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models 
• 4.9 Building Exponential, Logarithmic, and Logistic Models from Data 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

5. Trigonometric Functions 

• 5.1 Angles, Arc Length, and Circular Motion 
• 5.2 Trigonometric Functions: Unit Circle Approach 
• 5.3 Properties of the Trigonometric Functions 
• 5.4 Graphs of the Sine and Cosine Functions 
• 5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 
• 5.6 Phase Shift; Sinusoidal Curve Fitting 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

6. Analytic Trigonometry 

• 6.1 The Inverse Sine, Cosine, and Tangent Functions 
• 6.2 The Inverse Trigonometric Functions (Continued) 
• 6.3 Trigonometric Equations 
• 6.4 Trigonometric Identities 
• 6.5 Sum and Difference Formulas 
• 6.6 Double-angle and Half-angle Formulas 
• 6.7 Product-to-Sum and Sum-to-Product Formulas 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

7. Applications of Trigonometric Functions 

• 7.1 Right Triangle Trigonometry; Applications 
• 7.2 The Law of Sines 
• 7.3 The Law of Cosines 
• 7.4 Area of a Triangle 
• 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

8. Polar Coordinates; Vectors 

• 8.1 Polar Coordinates 
• 8.2 Polar Equations and Graphs 
• 8.3 The Complex Plane; De Moivre's Theorem 
• 8.4 Vectors 
• 8.5 The Dot Product 
• 8.6 Vectors in Space 
• 8.7 The Cross Product 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

9. Analytic Geometry 

• 9.1 Conics 
• 9.2 The Parabola 
• 9.3 The Ellipse 
• 9.4 The Hyperbola 
• 9.5 Rotation of Axes; General Form of a Conic 
• 9.6 Polar Equations of Conics 
• 9.7 Plane Curves and Parametric Equations 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

10. Systems of Equations and Inequalities 

• 10.1 Systems of Linear Equations: Substitution and Elimination 
• 10.2 Systems of Linear Equations: Matrices 
• 10.3 Systems of Linear Equations: Determinants 
• 10.4 Matrix Algebra 
• 10.5 Partial Fraction Decomposition 
• 10.6 Systems of Nonlinear Equations 
• 10.7 Systems of Inequalities 
• 10.8 Linear Programming 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

11. Sequences; Induction; the Binomial Theorem 

• 11.1 Sequences 
• 11.2 Arithmetic Sequences 
• 11.3 Geometric Sequences; Geometric Series 
• 11.4 Mathematical Induction 
• 11.5 The Binomial Theorem 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

12. Counting and Probability 

• 12.1 Counting 
• 12.2 Permutations and Combinations 
• 12.3 Probability 
• Chapter Review 
• Chapter Test 
• Cumulative Review 
• Chapter Projects 

13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function 

• 13.1 Investigating Limits Using Tables and Graphs 
• 13.2 Algebraic Techniques for Finding Limits 
• 13.3 One-sided Limits; Continuity 
• 13.4 The Tangent Problem; The Derivative 
• 13.5 The Area Problem; The Integral 
• Chapter Review 
• Chapter Test 
• Chapter Projects 

APPENDICES

• A. Review
• A.1 Algebra Essentials 
• A.2 Geometry Essentials 
• A.3 Polynomials 
• A.4 Factoring Polynomials 
• A.5 Synthetic Division 
• A.6 Rational Expressions 
• A.7 nth Roots; Rational Exponents
• A.8 Solving Equations 
• A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications 
• A.10 Interval Notation; Solving Inequalities 
• A.11 Complex Numbers 
• B. Graphing Utilities 
• B.1 The Viewing Rectangle 
• B.2 Using a Graphing Utility to Graph Equations 
• B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry 
• B.4 Using a Graphing Utility to Solve Equations 
• B.5 Square Screens 
• B.6 Using a Graphing Utility to Graph Inequalities 
• B.7 Using a Graphing Utility to Solve Systems of Linear Equations 
• B.8 Using a Graphing Utility to Graph a Polar Equation 
• B.9 Using a Graphing Utility to Graph Parametric Equations