# Precalculus: Functions and Graphs

Precalculus, Eighth Edition, provides the essential concepts and skills for students preparing to take calculus, as well as those students requiring college mathematics at this level to fulfill their degree requirements.

The book contains elements of reform, but within the context of a traditional curriculum. Topics are presented in a variety of ways - geometrically, graphically, numerically, symbolically, and analytically. Special attention is paid to pointing out the connection between algebraic and geometric interpretations of important concepts, which is effective in promoting visual thinking.

Special Features include:

• New, four-color interior design
• Real-world applications drawn from a variety of disciplines
• Graphing, incorporated throughout the text, promotes visualization
• Margin notes provide insight and advice to students
• The use of technology is optional, without compromising full coverage of the mathematics
• Problems are written and organized into three categories:

1. Providing the practice needed to master the concepts
2. A broad range of applications and models that require students to apply the concepts
3. Challenging students to develop and extend the concepts, while encouraging critical thinking and providing an excellent opportunity to stimulate class discussions that foster collaborative learning among students

Preface

Review of Basic Algebra - A Preliminary Chapter
Real Numbers
Polynomials
Factor Polynomials
Rational Expressions
Integer Exponents
Complex Numbers
Cumulative Review Problem Set

Chapter 1: Mathematical Models and Coordinate Geometry
Linear Equations and Mathematical Modeling
Nonlinear Equations
Inequalities
The Cartesian Coordinate System
Circles and Lines
Chapter 1 Review Problem Set
Chapter 1 Test

Chapter 2: Functions and Graphs
The Function Concept
Graphs of Functions
Graph Features
Transformations of Graphs
Combinations of Functions
Chapter 2 Review Problem Set
Chapter 2 Test

Chapter 3: Polynomial and Rational Functions
Polynomial Functions of Higher Degree
Polynomials and Their Division Properties
Rational Zeros
Irrational and Complex Zeros of Polynomial Functions
Rational Functions
Chapter 3 Review Problem Set
Chapter 3 Test

Chapter 4: Exponential and Logarithmic Functions
Inverse Functions
Exponential Functions
The Natural Base - Base eLogarithmic Functions
Properties of Logarithms
Chapter 4 Review Problem Set
Chapter 4 Test

Chapter 5: Trigonometric Functions
Angles and Arcs of Circles
Trigonometric Functions of Acute Angles and Modeling with Right Triangles
Trigonometric Functions of General Angles and Real Numbers
Properties of Trigonometric Functions
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Chapter 5 Review Problem Set
Chapter 5 Test

Chapter 6: Trigonometric Identities and Equations
Fundamental Identities
Double-Angle and Half-Angle Identities
Trigonometric Equations
Other Identities
Chapter 6 Review Problem Set
Chapter 6 Test

Chapter 7: Additional Applications of Trigonometry
The Law of Cosines and the Law of Sines
Introduction to Polar Coordinates
Vectors in the Plane
Trigonometric Forms of Complex Numbers
Chapter 7 Review Problem Set
Chapter 7 Test

Chapter 8: Systems of Equations and Inequalities
Solutions of Linear Systems by Substitution and Elimination
Solutions of Linear Systems Using Augmented Matrices
Solutions of Linear Systems Using Inverse Matrices
Solutions of Linear Systems Using Determinants
Solutions of Linear Systems of Inequalities and Linear Programming
Solutions of Nonlinear Systems of Equations and Inequalities
Chapter 8 Review Problem Set
Chapter 8 Test

Chapter 9: Topics in Analytic Geometry
Parabolas
Ellipses
Hyperbolas
Eccentricity and Polar Equation Forms for Conics
Rotation of Axes
Parametric Equations
Chapter 9 Review Problem Set
Chapter 9 Test

Chapter 10: Topics in Discrete Mathematics
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences and Series
Mathematical Induction
The Binomial Theorem
Chapter 10 Review Problem Set
Chapter 10 Test

Appendix 1: Plane Geometry Review
Appendix 2: Answers to Selected Problems
Index

Mustafa A Munem
James P Yizze

Precalculus, Eighth Edition, provides the essential concepts and skills for students preparing to take calculus, as well as those students requiring college mathematics at this level to fulfill their degree requirements.

The book contains elements of reform, but within the context of a traditional curriculum. Topics are presented in a variety of ways - geometrically, graphically, numerically, symbolically, and analytically. Special attention is paid to pointing out the connection between algebraic and geometric interpretations of important concepts, which is effective in promoting visual thinking.

Special Features include:

• New, four-color interior design
• Real-world applications drawn from a variety of disciplines
• Graphing, incorporated throughout the text, promotes visualization
• Margin notes provide insight and advice to students
• The use of technology is optional, without compromising full coverage of the mathematics
• Problems are written and organized into three categories:

1. Providing the practice needed to master the concepts
2. A broad range of applications and models that require students to apply the concepts
3. Challenging students to develop and extend the concepts, while encouraging critical thinking and providing an excellent opportunity to stimulate class discussions that foster collaborative learning among students

Preface

Review of Basic Algebra - A Preliminary Chapter
Real Numbers
Polynomials
Factor Polynomials
Rational Expressions
Integer Exponents
Complex Numbers
Cumulative Review Problem Set

Chapter 1: Mathematical Models and Coordinate Geometry
Linear Equations and Mathematical Modeling
Nonlinear Equations
Inequalities
The Cartesian Coordinate System
Circles and Lines
Chapter 1 Review Problem Set
Chapter 1 Test

Chapter 2: Functions and Graphs
The Function Concept
Graphs of Functions
Graph Features
Transformations of Graphs
Combinations of Functions
Chapter 2 Review Problem Set
Chapter 2 Test

Chapter 3: Polynomial and Rational Functions
Polynomial Functions of Higher Degree
Polynomials and Their Division Properties
Rational Zeros
Irrational and Complex Zeros of Polynomial Functions
Rational Functions
Chapter 3 Review Problem Set
Chapter 3 Test

Chapter 4: Exponential and Logarithmic Functions
Inverse Functions
Exponential Functions
The Natural Base - Base eLogarithmic Functions
Properties of Logarithms
Chapter 4 Review Problem Set
Chapter 4 Test

Chapter 5: Trigonometric Functions
Angles and Arcs of Circles
Trigonometric Functions of Acute Angles and Modeling with Right Triangles
Trigonometric Functions of General Angles and Real Numbers
Properties of Trigonometric Functions
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Chapter 5 Review Problem Set
Chapter 5 Test

Chapter 6: Trigonometric Identities and Equations
Fundamental Identities
Double-Angle and Half-Angle Identities
Trigonometric Equations
Other Identities
Chapter 6 Review Problem Set
Chapter 6 Test

Chapter 7: Additional Applications of Trigonometry
The Law of Cosines and the Law of Sines
Introduction to Polar Coordinates
Vectors in the Plane
Trigonometric Forms of Complex Numbers
Chapter 7 Review Problem Set
Chapter 7 Test

Chapter 8: Systems of Equations and Inequalities
Solutions of Linear Systems by Substitution and Elimination
Solutions of Linear Systems Using Augmented Matrices
Solutions of Linear Systems Using Inverse Matrices
Solutions of Linear Systems Using Determinants
Solutions of Linear Systems of Inequalities and Linear Programming
Solutions of Nonlinear Systems of Equations and Inequalities
Chapter 8 Review Problem Set
Chapter 8 Test

Chapter 9: Topics in Analytic Geometry
Parabolas
Ellipses
Hyperbolas
Eccentricity and Polar Equation Forms for Conics
Rotation of Axes
Parametric Equations
Chapter 9 Review Problem Set
Chapter 9 Test

Chapter 10: Topics in Discrete Mathematics
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences and Series
Mathematical Induction
The Binomial Theorem
Chapter 10 Review Problem Set
Chapter 10 Test

Appendix 1: Plane Geometry Review
Appendix 2: Answers to Selected Problems
Index

Mustafa A Munem
James P Yizze