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College Algebra 11th Edition by Michael Sullivan, ISBN-13: 978-0135163047

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College Algebra 11th Edition by Michael Sullivan, ISBN-13: 978-0135163047

[PDF eBook eTextbook]

  • Publisher: ‎ Pearson; 11th edition (March 4, 2019)
  • Language: ‎ English
  • 848 pages
  • ISBN-10: ‎ 0135163048
  • ISBN-13: ‎ 978-0135163047

For courses in College Algebra.

Prepare. Practice. Review.

Michael Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The 11th Edition continues to evolve to meet the needs of today’s students.

This series prepares and supports students with access to help, where and when they require it. The hallmark Sullivan cycle of continuous preparation and retention — along with the high-quality exercises that Sullivan texts are known for — gives students the reinforcement they need.

Table of Contents:

To the Student
Prepare for Class “Read the Book”
Practice “Work the Problems”
Review “Study for Quizzes and Tests”
College Algebra
Contents
Three Distinct Series
Flagship Series, Eleventh Edition
Enhanced with Graphing Utilities Series, Seventh Edition
Concepts through Functions Series, Fourth Edition
The Flagship Series
College Algebra, Eleventh Edition
Algebra & Trigonometry, Eleventh Edition
Precalculus, Eleventh Edition
Trigonometry: a Unit Circle Approach, Eleventh Edition
Preface to the Instructor
Features in the Eleventh Edition
Content Changes to the 11th edition
Using the Eleventh Edition Effectively with Your Syllabus
Get the Most Out of MyLab Math
Resources for Success MyLab Math Online Course for College Algebra, 11th Edition by Michael Sullivan (access code required)
Resources for Success
Instructor Resources
Instructor’s Solutions Manual
Learning Catalytics Question Library
Powerpoint® Lecture Slides
Mini Lecture Notes
Testgen®
Online Chapter Projects
Student Resources
Applications Index
R Review
Outline
R.1 Real Numbers
Preparing For This Text
1 Work with Sets
2 Classify Numbers
Approximations
Calculators and Graphing Utilities
Operations
3 Evaluate Numerical Expressions
4 Work with Properties of Real Numbers
R.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Explaining Concepts: Discussion and Writing
R.2 Algebra Essentials
Objectives
The Real Number Line
1 Graph Inequalities
2 Find Distance on the Real Number Line
3 Evaluate Algebraic Expressions
4 Determine the Domain of a Variable
5 Use the Laws of Exponents
6 Evaluate Square Roots
7 Use a Calculator to Evaluate Exponents
8 Use Scientific Notation
R.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
R.3 Geometry Essentials
1 Use the Pythagorean Theorem and Its Converse
2 Know Geometry Formulas
3 Understand Congruent Triangles and Similar Triangles
Proof of the Pythagorean Theorem
R.4 Polynomials
1 Recognize Monomials
2 Recognize Polynomials
3 Add and Subtract Polynomials
4 Multiply Polynomials
5 Know Formulas for Special Products
6 Divide Polynomials Using Long Division
7 Work with Polynomials in Two Variables
R.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Explaining Concepts: Discussion and Writing
R.5 Factoring Polynomials
1 Factor the Difference of Two Squares and the Sum and Difference of Two Cubes
2 Factor Perfect Squares
3 Factor a Second-Degree Polynomial: x2+Bx+C
4 Factor by Grouping
5 Factor a Second-Degree Polynomial: Ax2+Bx+C,A≠1
6 Complete the Square
R.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Mixed Practice
Applications and Extensions
Explaining Concepts: Discussion and Writing
R.6 Synthetic Division
1 Divide Polynomials Using Synthetic Division
R.6 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
R.7 Rational Expressions
1 Reduce a Rational Expression to Lowest Terms
2 Multiply and Divide Rational Expressions
3 Add and Subtract Rational Expressions
4 Use the Least Common Multiple Method
5 Simplify Complex Rational Expressions
Application
R.7 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
R.8 nth Roots; Rational Exponents
Preparing For This Section
Work with nth Roots
2 Simplify Radicals
3 Rationalize Denominators and Numerators
4 Simplify Expressions with Rational Exponents
R.8 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1 Equations and Inequalities
Outline
Financing a Purchase
1.1 Linear Equations
Preparing for This Section
Solving Equations Algebraically
1 Solve a Linear Equation
2 Solve Equations That Lead to Linear Equations
3 Solve Problems That Can Be Modeled by Linear Equations
1.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.2 Quadratic Equations
Preparing for This Section
1 Solve a Quadratic Equation by Factoring
2 Solve a Quadratic Equation Using the Square Root Method
3 Solve a Quadratic Equation by Completing the Square
4 Solve a Quadratic Equation Using the Quadratic Formula
5 Solve Problems That Can Be Modeled by Quadratic Equations
1.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.3 Complex Numbers; Quadratic Equations in the Complex Number System*
Preparing for This Section
Complex Numbers
1 Add, Subtract, Multiply, and Divide Complex Numbers
Conjugates
Powers of i
2 Solve Quadratic Equations in the Complex Number System
1.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
Preparing for This Section
1 Solve Radical Equations
2 Solve Equations Quadratic in Form
3 Solve Equations by Factoring
1.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Mixed Practice
Applications
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.5 Solving Inequalities
Preparing for This Section
1 Use Interval Notation
2 Use Properties of Inequalities
3 Solve Inequalities
4 Solve Combined Inequalities
Application
1.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.6 Equations and Inequalities Involving Absolute Value
Preparing for This Section
1 Solve Equations Involving Absolute Value
2 Solve Inequalities Involving Absolute Value
1.6 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
1 Translate Verbal Descriptions into Mathematical Expressions
2 Solve Interest Problems
3 Solve Mixture Problems
4 Solve Uniform Motion Problems
5 Solve Constant Rate Job Problems
1.7 Assess Your Understanding
Concepts and Vocabulary
Applications and Extensions
Explaining Concepts: Discussion and Writing
Chapter Review
Things to Know
Review Exercises
Chapter Test
2 Graphs
Outline
How to Value a House
Looking at “comps”
2.1 The Distance and Midpoint Formulas
Preparing for This Section
Rectangular Coordinates
1 Use the Distance Formula
2 Use the Midpoint Formula
2.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
Preparing for This Section
1 Graph Equations by Plotting Points
2 Find Intercepts from a Graph
3 Find Intercepts from an Equation
4 Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin
Know How to Graph Key Equations
2.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
2.3 Lines
1 Calculate and Interpret the Slope of a Line
2 Graph Lines Given a Point and the Slope
3 Find the Equation of a Vertical Line
4 Use the Point–Slope Form of a Line; Identify Horizontal Lines
5 Use the Slope-Intercept Form of a Line
6 Find the Equation of a Line Given Two Points
7 Graph Lines Written in General Form Using Intercepts
8 Find Equations of Parallel Lines
9 Find Equations of Perpendicular Lines
2.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
2.4 Circles
Preparing for This Section
1 Write the Standard Form of the Equation of a Circle
2 Graph a Circle
3 Work with the General Form of the Equation of a Circle
Overview
2.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
2.5 Variation
Objectives
1 Construct a Model Using Direct Variation
2 Construct a Model Using Inverse Variation
3 Construct a Model Using Joint Variation
2.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
Chapter Review
Things to Know
Objectives
Review Exercises
Chapter Test
Cumulative Review
3 Functions and Their Graphs
Outline
Choosing a Data Plan
3.1 Functions
Preparing for This Section
1 Describe a Relation
2 Determine Whether a Relation Represents a Function
3 Use Function Notation; Find the Value of a Function
Implicit Form of a Function
4 Find the Difference Quotient of a Function
5 Find the Domain of a Function Defined by an Equation
6 Form the Sum, Difference, Product, and Quotient of Two Functions
3.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
3.2 The Graph of a Function
Preparing for This Section
1 Identify the Graph of a Function
2 Obtain Information from or about the Graph of a Function
3.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
3.3 Properties of Functions
Preparing For This Section
1 Identify Even and Odd Functions from a Graph
2 Identify Even and Odd Functions from an Equation
3 Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant
4 Use a Graph to Locate Local Maxima and Local Minima
5 Use a Graph to Locate the Absolute Maximum and the Absolute Minimum
6 Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function Is Increasing or Decreasing
7 Find the Average Rate of Change of a Function
The Secant Line
3.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
3.4 Library of Functions; Piecewise-defined Functions
Preparing for This Section
1 Graph the Functions Listed in the Library of Functions
2 Analyze a Piecewise-defined Function
3.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
3.5 Graphing Techniques: Transformations
Objectives
1 Graph Functions Using Vertical and Horizontal Shifts
2 Graph Functions Using Compressions and Stretches
3 Graph Functions Using Reflections about the x-Axis and the y-Axis
3.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
3.6 Mathematical Models: Building Functions
Objective
1 Build and Analyze Functions
3.6 Assess Your Understanding
Applications and Extensions
Chapter Review
Library of Functions
Things to Know
Objectives
Review Exercises
Chapter Test
Cumulative Review
4 Linear and Quadratic Functions
Outline
The Beta of a Stock
4.1 Properties of Linear Functions and Linear Models
Preparing for This Section
1 Graph Linear Functions
2 Use Average Rate of Change to Identify Linear Functions
3 Determine Whether a Linear Function Is Increasing, Decreasing, or Constant
4 Build Linear Models from Verbal Descriptions
4.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
4.2 Building Linear Models from Data
Preparing for This Section
1 Draw and Interpret Scatter Plots
2 Distinguish between Linear and Nonlinear Relations
3 Use a Graphing Utility to Find the Line of Best Fit
4.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
4.3 Quadratic Functions and Their Properties
Preparing for This Section
Quadratic Functions
1 Graph a Quadratic Function Using Transformations
2 Identify the Vertex and Axis of Symmetry of a Parabola
3 Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts
4 Find a Quadratic Function Given Its Vertex and One Other Point
5 Find the Maximum or Minimum Value of a Quadratic Function
4.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
4.4 Building Quadratic Models from Verbal Descriptions and from Data
Preparing for This Section
1 Build Quadratic Models from Verbal Descriptions
2 Build Quadratic Models from Data
4.4 Assess Your Understanding
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
4.5 Inequalities Involving Quadratic Functions
Preparing for This Section
1 Solve Inequalities Involving a Quadratic Function
4.5 Assess Your Understanding
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
Chapter Review
Things to Know
Objectives
Review Exercises
Chapter Test
Cumulative Review
5 Polynomial and Rational Functions
Outline
Day Length
5.1 Polynomial Functions
Preparing for This Section
1 Identify Polynomial Functions and Their Degree
Power Functions
2 Graph Polynomial Functions Using Transformations
3 Identify the Real Zeros of a Polynomial Function and Their Multiplicity
Turning Points
End Behavior
5.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
5.2 Graphing Polynomial Functions; Models
Preparing for This Section
1 Graph a Polynomial Function
2 Graph a Polynomial Function Using a Graphing Utility
3 Build Cubic Models from Data
5.2 Assess Your Understanding
Skill Building
Applications and Extensions
‘Are You Prepared?’ Answers
5.3 Properties of Rational Functions
Preparing for This Section
1 Find the Domain of a Rational Function
Asymptotes
2 Find the Vertical Asymptotes of a Rational Function
Multiplicity and Vertical Asymptotes
3 Find a Horizontal or an Oblique Asymptote of a Rational Function
5.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
5.4 The Graph of a Rational Function
Preparing for This Section
1 Graph a Rational Function
2 Solve Applied Problems Involving Rational Functions
5.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Discussion and Writing
‘Are You Prepared?’ Answer
5.5 Polynomial and Rational Inequalities
Preparing for This Section
1 Solve Polynomial Inequalities
The Role of Multiplicity in Solving Polynomial Inequalities
2 Solve Rational Inequalities
The Role of Multiplicity in Solving Rational Inequalities
5.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
5.6 The Real Zeros of a Polynomial Function
Preparing for This Section
1 Use the Remainder and Factor Theorems
2 Use Descartes’ Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function
3 Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function
4 Find the Real Zeros of a Polynomial Function
5 Solve Polynomial Equations
6 Use the Theorem for Bounds on Zeros
7 Use the Intermediate Value Theorem
5.6 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
5.7 Complex Zeros; Fundamental Theorem of Algebra
Preparing for This Section
1 Use the Conjugate Pairs Theorem
2 Find a Polynomial Function with Specified Zeros
3 Find the Complex Zeros of a Polynomial Function
5.7 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
Chapter Review
Things to Know
Review Exercises
Chapter Test
Cumulative Review
6 Exponential and Logarithmic Functions
Outline
Depreciation of Cars
6.1 Composite Functions
Preparing for This Section
1 Form a Composite Function
2 Find the Domain of a Composite Function
Calculus Application
6.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
‘Are You Prepared?’ Answers
6.2 One-to-One Functions; Inverse Functions
Preparing For This Section
1 Determine Whether a Function Is One-to-One
2 Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function
3 Verify an Inverse Function
4 Find the Inverse of a Function Defined by an Equation
6.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
6.3 Exponential Functions
Preparing for This Section
1 Evaluate Exponential Functions
Introduction to Exponential Growth
2 Graph Exponential Functions
3 Define the Number e
4 Solve Exponential Equations
6.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
6.4 Logarithmic Functions
Preparing for This Section
1 Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements
2 Evaluate Logarithmic Expressions
3 Determine the Domain of a Logarithmic Function
4 Graph Logarithmic Functions
5 Solve Logarithmic Equations
6.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
6.5 Properties of Logarithms
1 Work with the Properties of Logarithms
6.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
6.6 Logarithmic and Exponential Equations
Preparing for This Section
1 Solve Logarithmic Equations
2 Solve Exponential Equations
3 Solve Logarithmic and Exponential Equations Using a Graphing Utility
6.6 Assess Your Understanding
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
6.7 Financial Models
Preparing For This Section
1 Determine the Future Value of a Lump Sum of Money
2 Calculate Effective Rates of Return
3 Determine the Present Value of a Lump Sum of Money
4 Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money
6.7 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
1 Model Populations That Obey the Law of Uninhibited Growth
2 Model Populations That Obey the Law of Uninhibited Decay
3 Use Newton’s Law of Cooling
4 Use Logistic Models
6.8 Assess Your Understanding
Applications and Extensions
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
Preparing for This Section
1 Build an Exponential Model from Data
2 Build a Logarithmic Model from Data
3 Build a Logistic Model from Data
6.9 Assess Your Understanding
Applications and Extensions
Chapter Review
Things to Know
Formulas
Objectives
Review Exercises
Chapter Test
Cumulative Review
7 Analytic Geometry
Outline
The Orbit of Comet Hale-Bopp
7.1 Conics
1 Know the Names of the Conics
7.2 The Parabola
Preparing for this Section
1 Analyze Parabolas with Vertex at the Origin
2 Analyze Parabolas with Vertex at (h, k)
3 Solve Applied Problems Involving Parabolas
7.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
‘Are You Prepared?’ Answers
7.3 The Ellipse
Preparing for this Section
1 Analyze Ellipses with Center at the Origin
2 Analyze Ellipses with Center at (h, k)
3 Solve Applied Problems Involving Ellipses
7.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Discussion and Writing
‘Are You Prepared?’ Answers
7.4 The Hyperbola
Preparing for this Section
1 Analyze Hyperbolas with Center at the Origin
2 Find the Asymptotes of a Hyperbola
3 Analyze Hyperbolas with Center at (h, k)
4 Solve Applied Problems Involving Hyperbolas
7.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
‘Are You Prepared?’ Answers
Chapter Review
Things to Know
Review Exercises
Chapter Test
Cumulative Review
8 Systems of Equations and Inequalities
Outline
Economic Outcomes Annual Earnings of Young Adults
8.1 Systems of Linear Equations: Substitution and Elimination
Preparing for This Section
1 Solve Systems of Equations by Substitution
2 Solve Systems of Equations by Elimination
3 Identify Inconsistent Systems of Equations Containing Two Variables
4 Express the Solution of a System of Dependent Equations Containing Two Variables
5 Solve Systems of Three Equations Containing Three Variables
6 Identify Inconsistent Systems of Equations Containing Three Variables
7 Express the Solution of a System of Dependent Equations Containing Three Variables
8.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
8.2 Systems of Linear Equations: Matrices
1 Write the Augmented Matrix of a System of Linear Equations
2 Write the System of Equations from the Augmented Matrix
3 Perform Row Operations on a Matrix
4 Solve a System of Linear Equations Using Matrices
8.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
8.3 Systems of Linear Equations: Determinants
1 Evaluate 2 by 2 Determinants
2 Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables
3 Evaluate 3 by 3 Determinants
4 Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables
5 Know Properties of Determinants
8.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
8.4 Matrix Algebra
1 Find the Sum and Difference of Two Matrices
2 Find Scalar Multiples of a Matrix
3 Find the Product of Two Matrices
8.4 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
8.5 Partial Fraction Decomposition
Preparing for this Section
1 Decompose PQ Where Q Has Only Nonrepeated Linear Factors
2 Decompose PQ Where Q Has Repeated Linear Factors
3 Decompose PQ Where Q Has a Nonrepeated Irreducible Quadratic Factor
4 Decompose PQ Where Q Has a Repeated Irreducible Quadratic Factor
8.5 Assess Your Understanding
Skill Building
‘Are You Prepared?’ Answers
8.6 Systems of Nonlinear Equations
Preparing for this Section
1 Solve a System of Nonlinear Equations Using Substitution
2 Solve a System of Nonlinear Equations Using Elimination
8.6 Assess Your Understanding
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
8.7 Systems of Inequalities
Preparing for this Section
1 Graph an Inequality
8.8 Linear Programming
1 Set Up a Linear Programming Problem
2 Solve a Linear Programming Problem
8.8 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
Chapter Review
Things to Know
Objectives
Review Exercises
Chapter Test
Cumulative Review
9 Sequences; Induction; the Binomial Theorem
Outline
World Population Projected to Reach 9.8 Billion by 2050
9.1 Sequences
Preparing for This Section
1 List the First Several Terms of a Sequence
The Factorial Symbol
2 List the Terms of a Sequence Defined by a Recursive Formula
3 Use Summation Notation
4 Find the Sum of a Sequence
9.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
9.2 Arithmetic Sequences
1 Determine Whether a Sequence Is Arithmetic
2 Find a Formula for an Arithmetic Sequence
3 Find the Sum of an Arithmetic Sequence
9.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
9.3 Geometric Sequences; Geometric Series
Preparing for This Section
1 Determine Whether a Sequence Is Geometric
2 Find a Formula for a Geometric Sequence
3 Find the Sum of a Geometric Sequence
4 Determine Whether a Geometric Series Converges or Diverges
5 Solve Annuity Problems
9.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
9.4 Mathematical Induction
1 Prove Statements Using Mathematical Induction
9.4 Assess Your Understanding
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
9.5 The Binomial Theorem
1 Evaluate (nj)
2 Use the Binomial Theorem
9.5 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Chapter Review
Things to Know
Objectives
Review Exercises
Chapter Test
Cumulative Review
10 Counting and Probability
Outline
Purchasing a Lottery Ticket
10.1 Counting
Preparing for This Section
1 Find All the Subsets of a Set
2 Count the Number of Elements in a Set
3 Solve Counting Problems Using the Multiplication Principle
10.1 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
10.2 Permutations and Combinations
Preparing for This Section
1 Solve Counting Problems Using Permutations Involving n Distinct Objects
2 Solve Counting Problems Using Combinations
3 Solve Counting Problems Using Permutations Involving n Nondistinct Objects
10.2 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Applications and Extensions
Explaining Concepts: Discussion and Writing
‘Are You Prepared?’ Answers
10.3 Probability
1 Construct Probability Models
2 Compute Probabilities of Equally Likely Outcomes
3 Find Probabilities of the Union of Two Events
4 Use the Complement Rule to Find Probabilities
10.3 Assess Your Understanding
Concepts and Vocabulary
Skill Building
Chapter Review
Things to Know
Review Exercises
Chapter Test
Cumulative Review
Appendix Graphing Utilities
Outline
1 The Viewing Rectangle
1 Exercises
2 Using a Graphing Utility to Graph Equations
2 Exercises
3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
Value and Zero (or Root)
3 Exercises
4 Using a Graphing Utility to Solve Equations
5 Square Screens
5 Exercises
6 Using a Graphing Utility to Graph Inequalities
7 Using a Graphing Utility to Solve Systems of Linear Equations
Answers
CHAPTER R Review
R.1 Assess Your Understanding (page 15)
R.2 Assess Your Understanding (page 26)
R.3 Assess Your Understanding (page 36)
R.4 Assess Your Understanding (page 47)
R.5 Assess Your Understanding (page 56)
R.6 Assess Your Understanding (page 60)
R.7 Assess Your Understanding (page 70)
R.8 Assess Your Understanding (page 78)
CHAPTER 1 Equations and Inequalities
1.1 Assess Your Understanding (page 90)
1.2 Assess Your Understanding (page 101)
1.3 Assess Your Understanding (page 111)
1.4 Assess Your Understanding (page 117)
1.5 Assess Your Understanding (page 127)
1.6 Assess Your Understanding (page 132)
1.7 Assess Your Understanding (page 140)
Review Exercises (page 145)
Chapter Test (page 147)
CHAPTER 2 Graphs
2.1 Assess Your Understanding (page 154)
2.2 Assess Your Understanding (page 166)
2.3 Assess Your Understanding (page 180)
2.4 Assess Your Understanding (page 188)
2.5 Assess Your Understanding (page 194)
Review Exercises (page 198)
Chapter Test (page 200)
Cumulative Review (page 200)
CHAPTER 3 Functions and Their Graphs
3.1 Assess Your Understanding (page 215)
3.2 Assess Your Understanding (page 223)
3.3 Assess Your Understanding (page 237)
3.4 Assess Your Understanding (page 250)
3.5 Assess Your Understanding (page 263)
3.6 Assess Your Understanding (page 270)
Review Exercises (page 275)
Chapter Test (page 277)
Cumulative Review (page 278)
CHAPTER 4 Linear and Quadratic Functions
4.1 Assess Your Understanding (page 287)
4.2 Assess Your Understanding (page 295)
4.3 Assess Your Understanding (page 308)
4.4 Assess Your Understanding (page 317)
4.5 Assess Your Understanding (page 323)
Review Exercises (page 325)
Chapter Test (page 327)
Cumulative Review (page 328)
CHAPTER 5 Polynomial and Rational Functions
5.1 Assess Your Understanding (page 343)
5.2 Assess Your Understanding (page 351)
5.3 Assess Your Understanding (page 362)
5.4 Assess Your Understanding (page 376)
5.5 Assess Your Understanding (page 384)
5.6 Assess Your Understanding (page 398)
5.7 Assess Your Understanding (page 406)
Review Exercises (page 410)
Chapter Test (page 411)
Cumulative Review (page 412)
CHAPTER 6 Exponential and Logarithmic Functions
6.1 Assess Your Understanding (page 419)
6.2 Assess Your Understanding (page 431)
6.3 Assess Your Understanding (page 446)
6.4 Assess Your Understanding (page 460)
6.5 Assess Your Understanding (page 471)
6.6 Assess Your Understanding (page 478)
6.7 Assess Your Understanding (page 487)
6.8 Assess Your Understanding (page 499)
6.8 Assess Your Understanding (page 499)
6.9 Assess Your Understanding (page 506)
Review Exercises (page 511)
Chapter Test (page 514)
Cumulative Review (page 515)
CHAPTER 7 Analytic Geometry
7.2 Assess Your Understanding (page 525)
7.3 Assess Your Understanding (page 535)
7.4 Assess Your Understanding (page 548)
Review Exercises (page 552)
Chapter Test (page 552)
Cumulative Review (page 553)
CHAPTER 8 Systems of Equations and Inequalities
8.1 Assess Your Understanding (page 566)
8.2 Assess Your Understanding (page 580)
8.3 Assess Your Understanding (page 592)
Historical Problems (page 608)
8.4 Assess Your Understanding (page 608)
8.5 Assess Your Understanding (page 619)
Historical Problem (page 626)
8.6 Assess Your Understanding (page 626)
8.7 Assess Your Understanding (page 635)
8.8 Assess Your Understanding (page 642)
Review Exercises (page 646)
Chapter Test (page 648)
Cumulative Review (page 649)
CHAPTER 9 Sequences; Induction; the Binomial Theorem
9.1 Assess Your Understanding (page 658)
9.2 Assess Your Understanding (page 666)
Historical Problems (page 676)
9.3 Assess Your Understanding (page 677)
9.4 Assess Your Understanding (page 683)
9.5 Assess Your Understanding (page 690)
Review Exercises (page 693)
Chapter Test (page 694)
Cumulative Review (page 694)
CHAPTER 10 Counting and Probability
10.1 Assess Your Understanding (page 701)
10.2 Assess Your Understanding (page 709)
Historical Problem (page 718)
10.3 Assess Your Understanding (page 718)
Review Exercises (page 722)
Chapter Test (page 723)
Cumulative Review (page 724)
APPENDIX Graphing Utilities
1 Exercises (page A2)
2 Exercises (page A4)
3 Exercises (page A6)
5 Exercises (page A8)
Photo Credits
Cover
Chapter R
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Subject Index
Conics
Parabola
Formulas/Equations
Geometry Formulas
Library of Functions
Functions

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.

Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

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