Precalculus

Table of Contents

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
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
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
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
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
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
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
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
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
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
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