# Precalculus: Functions and Graphs

**Author(s):**
Mustafa A
Munem
,
James P
Yizze

**Edition:
**
8

**Copyright:
**
2006

**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 theneeded to master the concepts*practice*

2. A broad range of applications and models that require students to*apply the concepts*

3. Challenging students to, while encouraging*develop and extend the concepts*and providing an excellent opportunity to stimulate class discussions that foster*critical thinking*among students*collaborative learning*

Preface** **

**Review of Basic Algebra - A
Preliminary Chapter**Real Numbers

Polynomials

Factor Polynomials

Rational Expressions

Integer Exponents

Radicals and Rational Exponents

Operations on Radical Expressions

Complex Numbers

Cumulative Review Problem Set

**C****hapter
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**Quadratic
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 *e*Logarithmic Functions

Properties of
Logarithms

Additional Equations and Inequalities

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

Addition and Subtraction 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

**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 theneeded to master the concepts*practice*

2. A broad range of applications and models that require students to*apply the concepts*

3. Challenging students to, while encouraging*develop and extend the concepts*and providing an excellent opportunity to stimulate class discussions that foster*critical thinking*among students*collaborative learning*

Preface** **

**Review of Basic Algebra - A
Preliminary Chapter**Real Numbers

Polynomials

Factor Polynomials

Rational Expressions

Integer Exponents

Radicals and Rational Exponents

Operations on Radical Expressions

Complex Numbers

Cumulative Review Problem Set

**C****hapter
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**Quadratic
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 *e*Logarithmic Functions

Properties of
Logarithms

Additional Equations and Inequalities

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

Addition and Subtraction 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