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Chapter 1 – Functions
- Introduction to Functions
- 1.1 Functions and Function Notation
- 1.2 Domain and Range
- 1.3 Rates of Change and Behavior of Graphs
- 1.4 Composition of Functions
- 1.5 Transformation of Functions
- 1.6 Absolute Value Functions
- 1.7 Inverse Functions
Chapter 2 – Linear Functions
- Introduction to Linear Functions
- 2.1 Linear Functions
- 2.2 Graphs of Linear Functions
- 2.3 Modeling with Linear Functions
- 2.4 Fitting Linear Models to Data
Chapter 3 – Polynomial and Rational Functions
- Introduction to Polynomial and Rational Functions
- 3.1 Complex Numbers
- 3.2 Quadratic Functions
- 3.3 Power Functions and Polynomial Functions
- 3.4 Graphs of Polynomial Functions
- 3.5 Dividing Polynomials
- 3.6 Zeros of Polynomial Functions
- 3.7 Rational Functions
- 3.8 Inverses and Radical Functions
- 3.9 Modeling Using Variation
Chapter 4 – Exponential and Logarithmic Functions
- Introduction to Exponential and Logarithmic Functions
- 4.1 Exponential Functions
- 4.2 Graphs of Exponential Functions
- 4.3 Logarithmic Functions
- 4.4 Graphs of Logarithmic Functions
- 4.5 Logarithmic Properties
- 4.6 Exponential and Logarithmic Equations
- 4.7 Exponential and Logarithmic Models
- 4.8 Fitting Exponential Models to Data
Chapter 5 – Trigonometric Functions
- Introduction to Trigonometric Functions
- 5.1 Angles
- 5.2 Unit Circle: Sine and Cosine Functions
- 5.3 The Other Trigonometric Functions
- 5.4 Right Triangle Trigonometry
Chapter 6 – Periodic Functions
- Introduction to Periodic Functions
- 6.1 Graphs of the Sine and Cosine Functions
- 6.2 Graphs of the Other Trigonometric Functions
- 6.3 Inverse Trigonometric Functions
Chapter 7 – Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 7.1 Solving Trigonometric Equations with Identities
- 7.2 Sum and Difference Identities
- 7.3 Double-Angle, Half-Angle, and Reduction Formulas
- 7.4 Sum-to-Product and Product-to-Sum Formulas
- 7.5 Solving Trigonometric Equations
- 7.6 Modeling with Trigonometric Equations
Chapter 8 – Further Applications of Trigonometry
- Introduction to Further Applications of Trigonometry
- 8.1 Non-right Triangles: Law of Sines
- 8.2 Non-right Triangles: Law of Cosines
- 8.3 Polar Coordinates
- 8.4 Polar Coordinates: Graphs
- 8.5 Polar Form of Complex Numbers
- 8.6 Parametric Equations
- 8.7 Parametric Equations: Graphs
- 8.8 Vectors
Chapter 9 – Systems of Equations and Inequalities
- Introduction to Systems of Equations and Inequalities
- 9.1 Systems of Linear Equations: Two Variables
- 9.2 Systems of Linear Equations: Three Variables
- 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
- 9.4 Partial Fractions
- 9.5 Matrices and Matrix Operations
- 9.6 Solving Systems with Gaussian Elimination
- 9.7 Solving Systems with Inverses
- 9.8 Solving Systems with Cramer’s Rule
Chapter 10 – Analytic Geometry
- Introduction to Analytic Geometry
- 10.1 The Ellipse
- 10.2 The Hyperbola
- 10.3 The Parabola
- 10.4 Rotation of Axes
- 10.5 Conic Sections in Polar Coordinates
Chapter 11 – Sequences, Probability and Counting Theory
- Introduction to Sequences, Probability and Counting Theory
- 11.1 Sequences and Their Notations
- 11.2 Arithmetic Sequences
- 11.3 Geometric Sequences
- 11.4 Series and Their Notations
- 11.5 Counting Principles
- 11.6 Binomial Theorem
- 11.7 Probability
Chapter 12 – Introduction to Calculus
- Introduction to Calculus
- 12.1 Finding Limits: Numerical and Graphical Approaches
- 12.2 Finding Limits: Properties of Limits
- 12.3 Continuity
- 12.4 Derivatives
