# Precalculus

### Course Info

Chapter 1 – FUNCTIONS AND THEIR GRAPHS

• 1.1  Lines in the Plane
• 1.2  Functions
• 1.3  Graphs of Functions
• 1.4  Shifting, Reflecting, and Stretching Graphs
• 1.5  Combinations of Functions
• 1.6  Inverse Functions
• 1.7  Linear Models and Scatter Plots

Chapter 2 – POLYNOMIAL AND RATIONAL FUNCTIONS

• 2.2  Polynomial Functions of Higher Degree
• 2.3  Real Zeros of Polynomial Functions
• 2.4  Complex Numbers
• 2.5  The Fundamental Theorem of Algebra
• 2.6  Rational Functions and Asymptotes
• 2.7  Graphs of Rational Functions

Chapter 3 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

• 3.1  Exponential Functions and Their Graphs
• 3.2  Logarithmic Functions and Their Graphs
• 3.3  Properties of Logarithms
• 3.4  Solving Exponential and Logarithmic Equations
• 3.5  Exponential and Logarithmic Models
• 3.6  Nonlinear Models

Chapter 4 – TRIGONOMETRIC FUNCTIONS

• 4.1  Radian and Degree Measure
• 4.2  Trigonometric Functions: The Unit Circle
• 4.3  Right Triangle Trigonometry
• 4.4  Trigonometric Functions of Any Angle
• 4.5  Graphs of Sine and Cosine Functions
• 4.6  Graphs of Other Trigonometric Functions
• 4.7  Inverse Trigonometric Functions
• 4.8  Applications and Models

Chapter 5 – ANALYTIC TRIGONOMETRY

• 5.1  Using Fundamental Identities
• 5.2  Verifying Trigonometric Identities
• 5.3  Solving Trigonometric Equations
• 5.4  Sum and Difference Formulas
• 5.5  Multiple-Angle and Product-to-Sum Formulas

Chapter 6 – ADDITIONAL TOPICS IN TRIGONOMETRY

• 6.1  Law of Sines
• 6.2  Law of Cosines
• 6.3  Vectors in the Plane
• 6.4  Vectors and Dot Products
• 6.5  Trigonometric Form of a Complex Number

Chapter 7 – LINEAR SYSTEMS AND MATRICES

• 7.1  Solving Systems of Equations
• 7.2  Systems of Linear Equations in Two Variables
• 7.3  Multivariable Linear Systems
• 7.4  Matrices and Systems of Equations
• 7.5  Operations with Matrices
• 7.6  The Inverse of a Square Matrix
• 7.7  The Determinant of a Square Matrix
• 7.8  Applications of Matrices and Determinants

Chapter 8 – SEQUENCES, SERIES, AND PROBABILITY

• 8.1  Sequences and Series
• 8.2  Arithmetic Sequences and Partial Sums
• 8.3  Geometric Sequences and Series
• 8.4  Mathematical Induction
• 8.5  The Binomial Theorem
• 8.6  Counting Principles
• 8.7  Probability

Chapter 9 – TOPICS IN ANALYTIC GEOMETRY

• 9.1  Circles and Parabolas
• 9.2  Ellipses
• 9.3  Hyperbolas
• 9.4  Rotation and Systems of Quadratic Equations
• 9.5  Parametric Equations
• 9.6  Polar Coordinates
• 9.7  Graphs of Polar Equations
• 9.8  Polar Equations of Conics

Chapter 10 – ANALYTIC GEOMETRY IN THREE DIMENSIONS

• 10.1  The Three-Dimensional Coordinate System
• 10.2  Vectors in Space
• 10.3  The Cross Product of Two Vectors
• 10.4  Lines and Planes in Space

Chapter 11 – LIMITS AND AN INTRODUCTION TO CALCULUS

• 11.1  Introduction to Limits
• 11.2  Techniques for Evaluating Limits
• 11.3  The Tangent Line Problem
• 11.4  Limits at Infinity and Limits of Sequences
• 11.5  The Area Problem

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