Precalculus: Graphs & Models
Chapter 1: Functions and Graphs
1.1, Rectangular Coordinates; Graphing Circles and Other Relations 1.2, Linear Equations and Rates of Change 1.3, Functions, Function Notation, and the Graph of a Function 1.4, Linear Functions, Special Forms, and More on Rates of Change 1.5, Solving Equations and Inequalities Graphically; Formulas and Problem Solving 1.6, Linear Function Models and Real Data
Chapter 2: Relations, More on Functions
2.1, Analyzing the Graph of a Function2.2, The Toolbox Functions and Transformations 2.3, Absolute Value Functions, Equations, and Inequalities2.4, Rational and Radical Functions; More on the Domain2.5, Piecewise-Defined Functions2.6, Variation: The Toolbox Functions in Action
Chapter 3: Quadratic Functions and Operations on Functions
3.1, Complex Numbers 3.2, Solving Quadratic Equations and Inequalities 3.3, Quadratic Functions and Applications 3.4, Quadratic Models; More on Rates of Change 3.5, The Algebra of Functions 3.6, Composition of Functions and the Difference Quotient
Chapter 4: Polynomial and Rational Functions
4.1, Synthetic Division; the Remainder and Factor Theorems 4.2, The Zeros of Polynomial Functions 4.3, Graphing Polynomial Functions 4.4, Graphing Rational Functions 4.5, Additional Insights into Rational Functions 4.6, Polynomial and Rational Inequalities
Chapter 5: Exponential and Logarithmic Functions
5.1, One-to-One and Inverse Functions 5.2, Exponential Functions 5.3, Logarithms and Logarithmic Functions 5.4, Properties of Logarithms 5.5, Solving Exponential and Logarithmic Equations 5.6, Applications from Business, Finance, and Science 5.7, Exponential, Logarithmic, and Logistic Equation Models
Chapter 6: Introduction to Trigonometry
6.1, Angle Measure, Special Triangles, and Special Angles 6.2, Unit Circles and the Trigonometry of Real Numbers 6.3, Graphs of Sine and Cosine Functions 6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions 6.5, Transformations and Applications of Trigonometric Graphs 6.6, The Trigonometry of Right Triangles 6.7, Trigonometry and the Coordinate Plane 6.8, Trigonometric Equation Models
Chapter 7: Trigonometric Identities, Inverses, and Equations
7.1, Fundamental Identities and Families of Identities 7.2, More on Verifying Identities 7.3, The Sum and Difference Identities 7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities 7.5, The Inverse Trigonometric Functions and their Applications 7.6, Solving Basic Trig Equations 7.7, General Trig Equations and Applications
Chapter 8: Applications of Trigonometry
8.1, Oblique Triangles and the Law of Sines 8.2, The Law of Cosines; the Area of a Triangle 8.3, Vectors and Vector Diagrams 8.4, Vector Applications and the Dot Product 8.5, Complex Numbers in Trigonometric Form 8.6, De Moivre's Theorem and the Theorem on nth Roots
Chapter 9: Systems of Equations ad Inequalities; Matrices
9.1, Linear Systems in Two Variables with Applications 9.2, Linear Systems in Three Variables with Applications 9.3, Systems of Inequalities and Linear Programming 9.4, Partial Fraction Decomposition 9.5, Solving Linear Systems Using Matrices and Row Operations 9.6, The Algebra of Matrices 9.7, Solving Linear Systems Using Matrix Equations 9.8, Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
Chapter 10: Analytical Geometry and the Conic Sections
10.1, A Brief Introduction to Analytic Geometry 10.2, The Circle and the Ellipse 10.3, The Hyperbola 10.4, The Analytic Parabola 10.5, Nonlinear Systems of Equations and Inequalities 10.6, Polar Coordinates, Equations, and Graphs 10.7, More on the Conic Sections: Rotation of Axes and Polar Form 10.8, Parametric Equations and Graphs
Chapter 11: Additional Topics in Algebra
11.1, Sequences and Series 11.2, Arithmetic Sequences 11.3, Geometric Sequences 11.4, Mathematical Induction 11.5, Counting Techniques 11.6, Introduction to Probability 11.7, The Binomial Theorem
Chapter 12: Bridges to Calculus - An Introduction to Limits
12.1, An Introduction to Limits Using Tables and Graphs 12.2, The Properties of Limits 12.3, Continuity and More on Limits 12.4, Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
Appendix A: A Review of Basic Concepts and Skills
A.1, Algebraic Expressions and the Properties of Real Numbers A.2, Exponents, Scientific Notation, and a Review of Polynomials A.3, Solving Linear Equations and Inequalities A.4, Factoring Polynomials and Solving Equations by Factoring A.5, Rational Expressions and Equations A.6, Radicals, Rational Exponents, and Radical Equations
Appendix B: Proof Positive - A Selection of Proofs from Precalculus Appendix C: More on Synthetic Division Appendix D: Reduced Row-Echelon Form and More on Matrices Appendix E: The Equation of a Conic Appendix F: Families of Polar Curves Online Appendices
AO.1, The Language, Notation, and Numbers of Mathematics AO.2, Geometry Review with Unit Conversions
