**Intermediate Algebra: Connecting Concepts through Applications, 2nd Edition**

By Mark Clark and Cynthia Anfinson

**Contents **

1 Linear Functions 1

1.1 Solving Linear Equations 2

Linear equations • Applications • Literal equations

1.2 Fundamentals of Graphing and Slope 19

Introduction to Graphing Equations • Linear Equations in Two Variables • The Meaning of Slope

in an Application • Graphing Lines Using Slope and Intercept

1.3 Intercepts and Graphing 41

The General Form of Lines • Intercepts and Their Meaning • Graphing Lines Using

Intercepts • Horizontal and Vertical Lines

1.4 Finding Equations of Lines 58

Equations of Lines • Parallel and Perpendicular Lines • Interpreting the Characteristics of

a Line: A Review

1.5 Functions and Function Notation 74

Relations and Functions • Vertical line test • Function Notation • Domain and Range of Functions

1.6 Using Data to Create Scatterplots 95

Using Data to Create Scatterplots • Adjusting Data • Graphical Models • Domain and Range of a

Model • Applications

1.7 Finding Linear Models 114

Using a Calculator to Create Scatterplots • Linear Models • Applications

Chapter 1 Summary 133

Chapter 1 Review Exercises 142

Chapter 1 Test 145

Chapter 1 Projects 146

Systems of Linear Equations and

Inequalities 149

2.1 Systems of Linear Equations 150

Definition of Systems • Graphical and Numerical Solutions • Types of Systems • Applications

2.2 Solving Systems of Equations Using the Substitution Method 166

Substitution Method • Consistent and Inconsistent Systems • Applications

2.3 Solving Systems of Equations Using the Elimination Method 179

Elimination Method • Applications of Systems

2.4 Solving Linear Inequalities 189

Introduction to Inequalities • Solving Inequalities • Systems as Inequalities • Solving

Inequalities Numerically and Graphically • Solving Compound Inequalities • Applications

2.5 Absolute Value Equations and Inequalities 205

Absolute Value Equations • Absolute Value Inequalities Involving “Less Than”

or “Less Than or Equal To” • Absolute Value Inequalities Involving “Greater Than”

or “Greater Than or Equal To” • Applications

2.6 Solving Systems of Linear Inequalities 220

Graphing Linear Inequalities with Two Variables • Solving Systems of Linear

Inequalities • Applications

Chapter 2 Summary 235

Chapter 2 Review Exercises 243

Chapter 2 Test 246

Chapter 2 Projects 248

Cumulative Review Chapters 1-2 250

3.1 Rules for Exponents 254

Rules for Exponents • Negative Exponents and Zero as an Exponent • Using Scientific

Notation • Rational exponents • Applications

3.2 Combining Functions 270

The Terminology of Polynomials • Degree • Adding and Subtracting Functions • Multiplying

and Dividing Functions • Applications

3.3 Composing Functions 288

Combining functions using composition • Applications

3.4 Factoring Polynomials 299

Factoring Out the GCF • Factoring by Grouping • Factoring Using the AC Method • Factoring

Using Trial and Error • Prime Polynomials

3.5 Special Factoring Techniques 312

Perfect Square Trinomials • Difference of Squares • Difference and Sum of Cubes • Multistep

Factorizations • Trinomials in Quadratic Form

Chapter 3 Summary 320

Chapter 3 Review Exercises 325

Chapter 3 Test 328

Chapter 3 Projects 330

4.1 Quadratic Functions and Parabolas 332

Introduction to Quadratic Functions and Identifying the Vertex • Identifying

a Quadratic Function • Recognizing Graphs of Quadratic Functions and Identifying the

Vertex • Applications

4.2 Graphing Quadratic Functions from Vertex Form 345

Axis of Symmetry • Vertex Form • Graphing Quadratic Functions from Vertex Form • Domain

and Range • Applications

4.3 Finding Quadratic Models 363

Quadratic Models • Domain and Range • Applications

4.4 Solving Quadratic Equations by the Square Root Property and

Completing the Square 378

Solving from Vertex Form • Square Root Property • Using the Pythagorean Theorem • The

Distance Formula • Completing the Square • Converting to Vertex Form • Graphing from

Vertex Form with x-Intercepts • Applications

4.5 Solving Equations by Factoring 399

The Product Property of Zero • Solving by Factoring • Finding a Quadratic Function from the

Graph • Solving Nonlinear Polynomial Inequalities in One Variable • Applications

4.6 Solving Quadratic Equations by Using the Quadratic Formula 417

Solving by the Quadratic Formula • Determining Which Algebraic Method to Use When Solving

a Quadratic Equation • Solving Systems of Equations Involving Quadratic Functions

4.7 Graphing Quadratic Functions from Standard Form 430

Graphing from Standard Form • Graphing Quadratic Inequalities in Two Variables • Applications

Chapter 4 Summary 444

Chapter 4 Review Exercises 457

Chapter 4 Test 461

Chapter 4 Projects 462

Cumulative Review Chapters 1-4 465

5.1 Exponential Functions: Patterns of Growth and Decay 470

Exploring Exponential Growth and Decay • Recognizing Exponential Patterns • Applications

5.2 Solving Equations Using Exponent Rules 489

Recap of the Rules for Exponents • Solving Power Equations • Solving Exponential Equations

by Inspection • Identifying Exponential Equations and Power Equations • Applications

5.3 Graphing Exponential Functions 498

Exploring Graphs of Exponentials • Domain and Range of Exponential

Functions • Exponentials of the Form f 1×2 5 a # bx 1 c

5.4 Finding Exponential Models 510

Exponential Functions • Exponential Models • Domain and Range for Exponential

Models • Applications

5.5 Exponential Growth and Decay Rates and Compounding Interest 523

Exponential Growth and Decay Rates • Compounding Interest • Growth Rates and

Exponential Functions • Applications

Chapter 5 Summary 534

Chapter 5 Review Exercises 539

Chapter 5 Test 541

Chapter 5 Projects 543

6.1 Functions and Their Inverses 548

Introduction to Inverse Functions • One-to-One Functions • Applications

6.2 Logarithmic Functions 561

Definition of Logarithms • Properties of Logarithms • Change of Base Formula • Inverses •

Equivalent Logarithm and Exponential Forms • Solving Logarithmic Equations

6.3 Graphing Logarithmic Functions 570

Graphing Logarithmic Functions • Domain and Range of Logarithmic Functions

6.4 Properties of Logarithms 578

Properties of Logarithms • Simplifying and Expanding Logarithm Expressions

6.5 Solving Exponential Equations 584

Solving Exponential Equations • Compounding Interest • Applications

6.6 Solving Logarithmic Equations 596

Solving Logarithmic Equations • Applications

Chapter 6 Summary 605

Chapter 6 Review Exercises 611

Chapter 6 Test 613

Chapter 6 Projects 614

Cumulative Review Chapters 1-6 616

7.1 Rational Functions and Variation 622

Rational Functions • Direct and Inverse Variation • Domain of a Rational

Function • Applications • Vertical Asymptotes and Holes in Graphs

7.2 Simplifying Rational Expressions 638

Simplifying Rational Expressions • Long Division of Polynomials • Synthetic

Division • Relationship between Division and Factoring

7.3 Multiplying and Dividing Rational Expressions 651

Multiplying Rational Expressions • Dividing Rational Expressions

7.4 Adding and Subtracting Rational Expressions 657

Least Common Denominator • Adding Rational Expressions • Subtracting Rational

Expressions • Simplifying Complex Fractions

7.5 Solving Rational Equations 668

Solving Rational Equations • Applications

Chapter 7 Summary 679

Chapter 7 Review Exercises 684

Chapter 7 Test 687

Chapter 7 Projects 688

8.1 Radical Functions 692

Relationships between Radicals and Rational Exponents • Radical Functions

That Model Data • Square Roots and Higher Roots • Simplifying Radicals • Applications

8.2 Graphing Radical Functions 705

Domain and Range of Radical Functions • Graphing Radical Functions • Odd and Even Indexes

8.3 Adding and Subtracting Radicals 715

Adding and Subtracting Radicals

8.4 Multiplying and Dividing Radicals 718

Multiplying Radicals • Dividing Radicals and Rationalizing the Denominator • Conjugates

8.5 Solving Radical Equations 729

Solving Radical Equations • Solving Radical Equations Involving more than One Square

Root • Extraneous Solution(s) • Solving Radical Equations Involving Higher-order

Roots • Applications

8.6 Complex Numbers 741

Definition of Imaginary and Complex Numbers • Operations with Complex Numbers • Solving

Equations with Complex Solutions

Chapter 8 Summary 751

Chapter 8 Review Exercises 756

Chapter 8 Test 759

Chapter 8 Projects 760

Cumulative Review Chapters 1-8 763

9.1 Parabolas and Circles 770

Introduction to Conic Sections • Revisiting Parabolas • A Geometric

Approach to Parabolas • Circles • Applications

9.2 Ellipses and Hyperbolas 791

Ellipses • Hyperbolas • Recognizing the Equations for Conic Sections • Applications

Chapter 9 Summary 805

Chapter 9 Review Exercises 809

Chapter 9 Test 811

Chapter 9 Projects 812

10.1 Arithmetic Sequences 816

Introduction to Sequences • Graphing Sequences • Arithmetic Sequences • Applications

10.2 Geometric Sequences 829

Geometric Sequences • Applications

10.3 Series 840

Introduction to Series • Arithmetic Series • Geometric Series • Applications

Chapter 10 Summary 850

Chapter 10 Review Exercises 853

Chapter 10 Test 855

Chapter 10 Projects 855

Basic Algebra Review A-1

Number Systems • Rectangular Coordinate System • Operations with Integers • Operations

with Rational Numbers • Order of Operations • Unit Conversions • Basic Solving

Techniques • Simplifying Square Roots • Interval Notation

Matrices B-1

Solving Systems of Three Equations • Matrices • Matrix Row Reduction • Solving Systems with

Matrices • Solving Systems of Three Equations to Model Quadratics

Using the Graphing Calculator C-1

Basic Keys and Calculations • Long Calculations • Converting Decimals to Fractions • Entering

Large Fractions • Absolute Values • Entering Logarithms with Different Bases • Entering

Radicals with Higher Indexes • Complex Number Calculations • Entering an Equation • Using

the Table Feature • Setting the Window • Graphing a Function • Tracing a Graph • Graphing a

Scatterplot • Graphing an Inequality with Shading • Error Messages • Additional Features • Zooming

to an Appropriate Window • Zero, Minimum, Maximum, and Intersect Features • Regression

Answers to Practice Problems D-1

Answers to Selected Exercises E-1

Index I-1

Unit Conversions REF-2

Geometric Formulas REF-3

Equation Solving Toolbox REF-4

Expression Simplifying Toolbox REF-5

Modeling Toolbox REF-6

Factoring Toolbox REF-6

1.1 Solving Linear Equations 2

Linear equations • Applications • Literal equations

1.2 Fundamentals of Graphing and Slope 19

Introduction to Graphing Equations • Linear Equations in Two Variables • The Meaning of Slope

in an Application • Graphing Lines Using Slope and Intercept

1.3 Intercepts and Graphing 41

The General Form of Lines • Intercepts and Their Meaning • Graphing Lines Using

Intercepts • Horizontal and Vertical Lines

1.4 Finding Equations of Lines 58

Equations of Lines • Parallel and Perpendicular Lines • Interpreting the Characteristics of

a Line: A Review

1.5 Functions and Function Notation 74

Relations and Functions • Vertical line test • Function Notation • Domain and Range of Functions

1.6 Using Data to Create Scatterplots 95

Using Data to Create Scatterplots • Adjusting Data • Graphical Models • Domain and Range of a

Model • Applications

1.7 Finding Linear Models 114

Using a Calculator to Create Scatterplots • Linear Models • Applications

Chapter 1 Summary 133

Chapter 1 Review Exercises 142

Chapter 1 Test 145

Chapter 1 Projects 146

Systems of Linear Equations and

Inequalities 149

2.1 Systems of Linear Equations 150

Definition of Systems • Graphical and Numerical Solutions • Types of Systems • Applications

2.2 Solving Systems of Equations Using the Substitution Method 166

Substitution Method • Consistent and Inconsistent Systems • Applications

2.3 Solving Systems of Equations Using the Elimination Method 179

Elimination Method • Applications of Systems

2.4 Solving Linear Inequalities 189

Introduction to Inequalities • Solving Inequalities • Systems as Inequalities • Solving

Inequalities Numerically and Graphically • Solving Compound Inequalities • Applications

2.5 Absolute Value Equations and Inequalities 205

Absolute Value Equations • Absolute Value Inequalities Involving “Less Than”

or “Less Than or Equal To” • Absolute Value Inequalities Involving “Greater Than”

or “Greater Than or Equal To” • Applications

2.6 Solving Systems of Linear Inequalities 220

Graphing Linear Inequalities with Two Variables • Solving Systems of Linear

Inequalities • Applications

Chapter 2 Summary 235

Chapter 2 Review Exercises 243

Chapter 2 Test 246

Chapter 2 Projects 248

Cumulative Review Chapters 1-2 250

3.1 Rules for Exponents 254

Rules for Exponents • Negative Exponents and Zero as an Exponent • Using Scientific

Notation • Rational exponents • Applications

3.2 Combining Functions 270

The Terminology of Polynomials • Degree • Adding and Subtracting Functions • Multiplying

and Dividing Functions • Applications

3.3 Composing Functions 288

Combining functions using composition • Applications

3.4 Factoring Polynomials 299

Factoring Out the GCF • Factoring by Grouping • Factoring Using the AC Method • Factoring

Using Trial and Error • Prime Polynomials

3.5 Special Factoring Techniques 312

Perfect Square Trinomials • Difference of Squares • Difference and Sum of Cubes • Multistep

Factorizations • Trinomials in Quadratic Form

Chapter 3 Summary 320

Chapter 3 Review Exercises 325

Chapter 3 Test 328

Chapter 3 Projects 330

4.1 Quadratic Functions and Parabolas 332

Introduction to Quadratic Functions and Identifying the Vertex • Identifying

a Quadratic Function • Recognizing Graphs of Quadratic Functions and Identifying the

Vertex • Applications

4.2 Graphing Quadratic Functions from Vertex Form 345

Axis of Symmetry • Vertex Form • Graphing Quadratic Functions from Vertex Form • Domain

and Range • Applications

4.3 Finding Quadratic Models 363

Quadratic Models • Domain and Range • Applications

4.4 Solving Quadratic Equations by the Square Root Property and

Completing the Square 378

Solving from Vertex Form • Square Root Property • Using the Pythagorean Theorem • The

Distance Formula • Completing the Square • Converting to Vertex Form • Graphing from

Vertex Form with x-Intercepts • Applications

4.5 Solving Equations by Factoring 399

The Product Property of Zero • Solving by Factoring • Finding a Quadratic Function from the

Graph • Solving Nonlinear Polynomial Inequalities in One Variable • Applications

4.6 Solving Quadratic Equations by Using the Quadratic Formula 417

Solving by the Quadratic Formula • Determining Which Algebraic Method to Use When Solving

a Quadratic Equation • Solving Systems of Equations Involving Quadratic Functions

4.7 Graphing Quadratic Functions from Standard Form 430

Graphing from Standard Form • Graphing Quadratic Inequalities in Two Variables • Applications

Chapter 4 Summary 444

Chapter 4 Review Exercises 457

Chapter 4 Test 461

Chapter 4 Projects 462

Cumulative Review Chapters 1-4 465

5.1 Exponential Functions: Patterns of Growth and Decay 470

Exploring Exponential Growth and Decay • Recognizing Exponential Patterns • Applications

5.2 Solving Equations Using Exponent Rules 489

Recap of the Rules for Exponents • Solving Power Equations • Solving Exponential Equations

by Inspection • Identifying Exponential Equations and Power Equations • Applications

5.3 Graphing Exponential Functions 498

Exploring Graphs of Exponentials • Domain and Range of Exponential

Functions • Exponentials of the Form f 1×2 5 a # bx 1 c

5.4 Finding Exponential Models 510

Exponential Functions • Exponential Models • Domain and Range for Exponential

Models • Applications

5.5 Exponential Growth and Decay Rates and Compounding Interest 523

Exponential Growth and Decay Rates • Compounding Interest • Growth Rates and

Exponential Functions • Applications

Chapter 5 Summary 534

Chapter 5 Review Exercises 539

Chapter 5 Test 541

Chapter 5 Projects 543

6.1 Functions and Their Inverses 548

Introduction to Inverse Functions • One-to-One Functions • Applications

6.2 Logarithmic Functions 561

Definition of Logarithms • Properties of Logarithms • Change of Base Formula • Inverses •

Equivalent Logarithm and Exponential Forms • Solving Logarithmic Equations

6.3 Graphing Logarithmic Functions 570

Graphing Logarithmic Functions • Domain and Range of Logarithmic Functions

6.4 Properties of Logarithms 578

Properties of Logarithms • Simplifying and Expanding Logarithm Expressions

6.5 Solving Exponential Equations 584

Solving Exponential Equations • Compounding Interest • Applications

6.6 Solving Logarithmic Equations 596

Solving Logarithmic Equations • Applications

Chapter 6 Summary 605

Chapter 6 Review Exercises 611

Chapter 6 Test 613

Chapter 6 Projects 614

Cumulative Review Chapters 1-6 616

7.1 Rational Functions and Variation 622

Rational Functions • Direct and Inverse Variation • Domain of a Rational

Function • Applications • Vertical Asymptotes and Holes in Graphs

7.2 Simplifying Rational Expressions 638

Simplifying Rational Expressions • Long Division of Polynomials • Synthetic

Division • Relationship between Division and Factoring

7.3 Multiplying and Dividing Rational Expressions 651

Multiplying Rational Expressions • Dividing Rational Expressions

7.4 Adding and Subtracting Rational Expressions 657

Least Common Denominator • Adding Rational Expressions • Subtracting Rational

Expressions • Simplifying Complex Fractions

7.5 Solving Rational Equations 668

Solving Rational Equations • Applications

Chapter 7 Summary 679

Chapter 7 Review Exercises 684

Chapter 7 Test 687

Chapter 7 Projects 688

8.1 Radical Functions 692

Relationships between Radicals and Rational Exponents • Radical Functions

That Model Data • Square Roots and Higher Roots • Simplifying Radicals • Applications

8.2 Graphing Radical Functions 705

Domain and Range of Radical Functions • Graphing Radical Functions • Odd and Even Indexes

8.3 Adding and Subtracting Radicals 715

Adding and Subtracting Radicals

8.4 Multiplying and Dividing Radicals 718

Multiplying Radicals • Dividing Radicals and Rationalizing the Denominator • Conjugates

8.5 Solving Radical Equations 729

Solving Radical Equations • Solving Radical Equations Involving more than One Square

Root • Extraneous Solution(s) • Solving Radical Equations Involving Higher-order

Roots • Applications

8.6 Complex Numbers 741

Definition of Imaginary and Complex Numbers • Operations with Complex Numbers • Solving

Equations with Complex Solutions

Chapter 8 Summary 751

Chapter 8 Review Exercises 756

Chapter 8 Test 759

Chapter 8 Projects 760

Cumulative Review Chapters 1-8 763

9.1 Parabolas and Circles 770

Introduction to Conic Sections • Revisiting Parabolas • A Geometric

Approach to Parabolas • Circles • Applications

9.2 Ellipses and Hyperbolas 791

Ellipses • Hyperbolas • Recognizing the Equations for Conic Sections • Applications

Chapter 9 Summary 805

Chapter 9 Review Exercises 809

Chapter 9 Test 811

Chapter 9 Projects 812

10.1 Arithmetic Sequences 816

Introduction to Sequences • Graphing Sequences • Arithmetic Sequences • Applications

10.2 Geometric Sequences 829

Geometric Sequences • Applications

10.3 Series 840

Introduction to Series • Arithmetic Series • Geometric Series • Applications

Chapter 10 Summary 850

Chapter 10 Review Exercises 853

Chapter 10 Test 855

Chapter 10 Projects 855

Basic Algebra Review A-1

Number Systems • Rectangular Coordinate System • Operations with Integers • Operations

with Rational Numbers • Order of Operations • Unit Conversions • Basic Solving

Techniques • Simplifying Square Roots • Interval Notation

Matrices B-1

Solving Systems of Three Equations • Matrices • Matrix Row Reduction • Solving Systems with

Matrices • Solving Systems of Three Equations to Model Quadratics

Using the Graphing Calculator C-1

Basic Keys and Calculations • Long Calculations • Converting Decimals to Fractions • Entering

Large Fractions • Absolute Values • Entering Logarithms with Different Bases • Entering

Radicals with Higher Indexes • Complex Number Calculations • Entering an Equation • Using

the Table Feature • Setting the Window • Graphing a Function • Tracing a Graph • Graphing a

Scatterplot • Graphing an Inequality with Shading • Error Messages • Additional Features • Zooming

to an Appropriate Window • Zero, Minimum, Maximum, and Intersect Features • Regression

Answers to Practice Problems D-1

Answers to Selected Exercises E-1

Index I-1

Unit Conversions REF-2

Geometric Formulas REF-3

Equation Solving Toolbox REF-4

Expression Simplifying Toolbox REF-5

Modeling Toolbox REF-6

Factoring Toolbox REF-6