Chapter 1: Graphs, Functions, and Models
1.1: Introduction to Graphing
1.2: Functions and Graphs
1.3: Linear Functions, Slope, and Applications
1.4: Equations of Lines and Modeling
1.5: Linear Equations, Functions, Zeros, and Applications
1.6: Solving Linear Inequalities
Chapter 2: More on Functions
2.1: Increasing, Decreasing, and Piecewise Functions; Applications
2.2: The Algebra of Functions
2.3: The Composition of Functions
2.4: Symmetry
2.5: Transformations
2.6: Variation and Applications
Chapter 3: Quadratic Functions and Equations; Inequalities
3.1: The Complex Numbers
3.2: Quadratic Equations, Functions, Zeros, and Models
3.3: Analyzing Graphs of Quadratic Functions
3.4: Solving Rational Equations and Radical Equations
3.5: Solving Equations and Inequalities with Absolute Value
Chapter 4: Polynomial Functions and Rational Functions
4.1: Polynomial Functions and Models
4.2: Graphing Polynomial Functions
4.3: Polynomial Division; The Remainder Theorem and the Factor Theorem
4.4: Theorems about Zeros of Polynomial Functions
4.5: Rational Functions
4.6: Polynomial Inequalities and Rational Inequalities
Chapter 5: Exponential Functions and Logarithmic Functions
5.1: Inverse Functions
5.2: Exponential Functions and Graphs
5.3: Logarithmic Functions and Graphs
5.4: Properties of Logarithmic Functions
5.5: Solving Exponential Equations and Logarithmic Equations
5.6: Applications and Models: Growth and Decay; Compound Interest
Chapter 6: The Trigonometric Functions
6.1: Trigonometric Functions of Acute Angles
6.2: Applications of Right Triangles
6.3: Trigonometric Functions of Any Angle
6.4: Radians, Arc Length, and Angular Speed
6.5: Circular Functions: Graphs and Properties
6.6: Graphs of Transformed Sine and Cosine Functions
Chapter 7: Trigonometric Identities, Inverse Functions, and Equations
7.1: Identities: Pythagorean and Sum and Difference
7.2: Identities: Cofunction, Double-Angle, and Half-Angle
7.3: Proving Trigonometric Identities
7.4: Inverses of the Trigonometric Functions
7.5: Solving Trigonometric Equations
Chapter 8: Applications of Trigonometry
8.1: The Law of Sines
8.2: The Law of Cosines
8.3: Complex Numbers: Trigonometric Notation
8.4: Polar Coordinates and Graphs
8.5: Vectors and Applications
8.6: Vector Operations
Chapter 9: Systems of Equations and Matrices
9.1: Systems of Equations in Two Variables
9.2: Systems of Equations in Three Variables
9.3: Matrices and Systems of Equations
9.4: Matrix Operations
9.5: Inverses of Matrices
9.6: Determinants and Cramer’s Rule
9.7: Systems of Inequalities and Linear Programming
9.8: Partial Fractions
Chapter 10: Conic Sections
10.1: The Parabola
10.2: The Circle and the Ellipse
10.3: The Hyperbola
10.4: Nonlinear Systems of Equations and Inequalities
10.5: Rotation of Axes
10.6: Polar Equations of Conics
10.7: Parametric Equations
Chapter 11: Sequences, Series, and Combinatorics
11.1: Sequences and Series
11.2: Arithmetic Sequences and Series
11.3: Geometric Sequences and Series
11.4: Mathematical Induction
11.5: Combinatorics: Permutations
11.6: Combinatorics: Combinations
11.7: The Binomial Theorem
11.8: Probability
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