Precalculus

Table of Contents
Preface
Relations and Functions
Sets of Real Numbers and the Cartesian Coordinate Plane
Sets of Numbers
The Cartesian Coordinate Plane
Distance in the Plane
Exercises
Answers
Relations
Graphs of Equations
Exercises
Answers
Introduction to Functions
Exercises
Answers
Function Notation
Modeling with Functions
Exercises
Answers
Function Arithmetic
Exercises
Answers
Graphs of Functions
General Function Behavior
Exercises
Answers
Transformations
Exercises
Answers
Linear and Quadratic Functions
Linear Functions
Exercises
Answers
Absolute Value Functions
Exercises
Answers
Quadratic Functions
Exercises
Answers
Inequalities with Absolute Value and Quadratic Functions
Exercises
Answers
Regression
Exercises
Answers
Polynomial Functions
Graphs of Polynomials
Exercises
Answers
The Factor Theorem and the Remainder Theorem
Exercises
Answers
Real Zeros of Polynomials
For Those Wishing to use a Graphing Calculator
For Those Wishing NOT to use a Graphing Calculator
Exercises
Answers
Complex Zeros and the Fundamental Theorem of Algebra
Exercises
Answers
Rational Functions
Introduction to Rational Functions
Exercises
Answers
Graphs of Rational Functions
Exercises
Answers
Rational Inequalities and Applications
Variation
Exercises
Answers
Further Topics in Functions
Function Composition
Exercises
Answers
Inverse Functions
Exercises
Answers
Other Algebraic Functions
Exercises
Answers
Exponential and Logarithmic Functions
Introduction to Exponential and Logarithmic Functions
Exercises
Answers
Properties of Logarithms
Exercises
Answers
Exponential Equations and Inequalities
Exercises
Answers
Logarithmic Equations and Inequalities
Exercises
Answers
Applications of Exponential and Logarithmic Functions
Applications of Exponential Functions
Applications of Logarithms
Exercises
Answers
Hooked on Conics
Introduction to Conics
Circles
Exercises
Answers
Parabolas
Exercises
Answers
Ellipses
Exercises
Answers
Hyperbolas
Exercises
Answers
Systems of Equations and Matrices
Systems of Linear Equations: Gaussian Elimination
Exercises
Answers
Systems of Linear Equations: Augmented Matrices
Exercises
Answers
Matrix Arithmetic
Exercises
Answers
Systems of Linear Equations: Matrix Inverses
Exercises
Answers
Determinants and Cramer's Rule
Definition and Properties of the Determinant
Cramer's Rule and Matrix Adjoints
Exercises
Answers
Partial Fraction Decomposition
Exercises
Answers
Systems of Non-Linear Equations and Inequalities
Exercises
Answers
Sequences and the Binomial Theorem
Sequences
Exercises
Answers
Summation Notation
Exercises
Answers
Mathematical Induction
Exercises
Selected Answers
The Binomial Theorem
Exercises
Answers
Foundations of Trigonometry
Angles and their Measure
Applications of Radian Measure: Circular Motion
Exercises
Answers
The Unit Circle: Cosine and Sine
Beyond the Unit Circle
Exercises
Answers
The Six Circular Functions and Fundamental Identities
Beyond the Unit Circle
Exercises
Answers
Trigonometric Identities
Exercises
Answers
Graphs of the Trigonometric Functions
Graphs of the Cosine and Sine Functions
Graphs of the Secant and Cosecant Functions
Graphs of the Tangent and Cotangent Functions
Exercises
Answers
The Inverse Trigonometric Functions
Inverses of Secant and Cosecant: Trigonometry Friendly Approach
Inverses of Secant and Cosecant: Calculus Friendly Approach
Calculators and the Inverse Circular Functions.
Solving Equations Using the Inverse Trigonometric Functions.
Exercises
Answers
Trigonometric Equations and Inequalities
Exercises
Answers
Applications of Trigonometry
Applications of Sinusoids
Harmonic Motion
Exercises
Answers
The Law of Sines
Exercises
Answers
The Law of Cosines
Exercises
Answers
Polar Coordinates
Exercises
Answers
Graphs of Polar Equations
Exercises
Answers
Hooked on Conics Again
Rotation of Axes
The Polar Form of Conics
Exercises
Answers
Polar Form of Complex Numbers
Exercises
Answers
Vectors
Exercises
Answers
The Dot Product and Projection
Exercises
Answers
Parametric Equations
Exercises
Answers
Index