Precalculus: Graphs & Models
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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 Function

2.2, The Toolbox Functions and Transformations

2.3, Absolute Value Functions, Equations, and Inequalities

2.4, Rational and Radical Functions; More on the Domain

2.5, Piecewise-Defined Functions

2.6, 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