## Precalculus Graphical, Numerical, Algebraic, Tenth Edition

By Franklin D. Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy and David E. Bock

**Contents:**

Chapter P Prerequisites

P.1 Real Numbers 26

Representing Real Numbers • Order and Interval Notation • Basic

Properties of Algebra • Integer Exponents • Scientific Notation

P.2 Cartesian Coordinate System 36

Cartesian Plane • Absolute Value of a Real Number • Distance Formulas •

Midpoint Formulas • Equations of Circles • Applications

P.3 Linear Equations and Inequalities 45

Equations • Solving Equations • Linear Equations in One Variable

• Linear Inequalities in One Variable

P.4 Lines in the Plane 52

Slope of a Line • Point-Slope Form Equation of a Line • Slope-Intercept

Form Equation of a Line • Graphing Linear Equations in Two Variables

Parallel and Perpendicular Lines • Applying Linear Equations in Two Variables

P.5 Solving Equations Graphically, Numerically, and Algebraically 64

Solving Equations Graphically • Solving Quadratic Equations •

Approximating Solutions of Equations Graphically • Approximating

Solutions of Equations Numerically Using Tables • Solving Equations by Finding Intersections

P.6 Complex Numbers 72

Complex Numbers • Operations with Complex Numbers • Complex

Conjugates and Division • Complex Solutions of Quadratic Equations

P.7 Solving Inequalities Algebraically and Graphically 77

Solving Absolute Value Inequalities • Solving Quadratic Inequalities •

Approximating Solutions to Inequalities • Projectile Motion

Key Ideas 82

Review Exercises 82

Chapter-1 Functions and Graphs

1.1 Modeling and Equation Solving 86

Numerical Models • Algebraic Models • Graphical Models • The Zero

Factor Property • Problem Solving • Grapher Failure and Hidden Behavior

• A Word About Proof

1.2 Functions and Their Properties 102

Function Definition and Notation • Domain and Range • Continuity •

Increasing and Decreasing Functions • Boundedness • Local and Absolute

Extrema • Symmetry • Asymptotes • End Behavior

1.3 Twelve Basic Functions 120

What Graphs Can Tell Us • Twelve Basic Functions • Analyzing Functions Graphically

1.4 Building Functions from Functions 130

Combining Functions Algebraically • Composition of Functions

• Relations and Implicitly Defined Functions

1.5 Parametric Relations and Inverses 139

Relations Defined Parametrically • Inverse Relations and Inverse Functions

1.6 Graphical Transformations 148

Transformations • Vertical and Horizontal Translations • Reflections

Across Axes • Vertical and Horizontal Stretches and Shrinks • Combining Transformations

1.7 Modeling with Functions 159

Functions from Formulas • Functions from Graphs • Functions from Verbal Descriptions

• Functions from Data

Key Ideas 171

Review Exercises 171

Modeling Project 174

CHAPTER 2 Polynomial, Power, and Rational Functions

2.1 Linear and Quadratic Functions and Modeling 176

Polynomial Functions • Linear Functions and Their Graphs • Average Rate

of Change • Association, Correlation, and Linear Modeling • Quadratic

Functions and Their Graphs • Applications of Quadratic Functions • Graphical Transformations

2.2 Modeling with Power Functions 193

Power Functions and Variation • Monomial Functions and Their Graphs •

Graphs of Power Functions • Modeling with Power Functions

2.3 Polynomial Functions of Higher Degree with Modeling 204

Graphs of Polynomial Functions • End Behavior of Polynomial Functions •

Zeros of Polynomial Functions • Intermediate Value Theorem • Modeling

2.4 Real Zeros of Polynomial Functions 216

Long Division and the Division Algorithm • Remainder and Factor

Theorems • Synthetic Division • Rational Zeros Theorem • Upper and Lower Bounds

2.5 Complex Zeros and the Fundamental Theorem of Algebra 228

Two Major Theorems • Complex Conjugate Zeros • Factoring with Real Number Coefficients

2.6 Graphs of Rational Functions 236

Rational Functions • Transformations of the Reciprocal Function •

Limits and Asymptotes • Analyzing Graphs of Rational Functions •

Transformations of Rational Functions • Exploring Relative Humidity

2.7 Solving Equations in One Variable 247

Solving Rational Equations • Extraneous Solutions • Applications

2.8 Solving Inequalities in One Variable 255

Polynomial Inequalities • Rational Inequalities • Other Inequalities • Applications

Key Ideas 264

Review Exercises 265

Modeling Project 268

CHAPTER 3 Exponential, Logistic, and Logarithmic Functions

3.1 Exponential and Logistic Functions 270

Exponential Functions and Their Graphs • The Natural Base e • Logistic Functions and Their Graphs

• Population Models

3.2 Exponential and Logistic Modeling 283

Constant Percentage Rate and Exponential Functions • Exponential

Growth and Decay Models • Using Regression to Model Population • Other Logistic Models

3.3 Logarithmic Functions and Their Graphs 292

Inverses of Exponential Functions • Common Logarithms—Base 10

Natural Logarithms—Base e • Graphs of Logarithmic Functions

• Measuring Sound Using Decibels

3.4 Properties of Logarithmic Functions 301

Properties of Logarithms • Change of Base • Graphs of Logarithmic Functions with Base b

• Re-expressing Data

3.5 Equation Solving and Modeling 310

Solving Exponential Equations • Solving Logarithmic Equations • Orders

of Magnitude and Logarithmic Models • Newton’s Law of Cooling

• Logarithmic Re-expression

3.6 Mathematics of Finance 322

Simple and Compound Interest • Interest Compounded k Times per

Year • Interest Compounded Continuously • Annual Percentage Yield •

Annuities—Future Value • Loans and Mortgages—Present Value

Key Ideas 331

Review Exercises 332

Modeling Project 335

CHAPTER 4 Trigonometric Functions

4.1 Angles and Their Measures 337

The Problem of Angular Measure • Degrees and Radians • Circular Arc Length

• Angular and Linear Motion

4.2 Trigonometric Functions of Acute Angles 346

Right Triangle Trigonometry • Two Famous Triangles • Evaluating

Trigonometric Functions with a Calculator • Common Calculator

Errors When Evaluating Trig Functions • Applications of Right Triangle Trigonometry

4.3 Trigonometry Extended: The Circular Functions 355

Trigonometric Functions of Any Angle • Trigonometric Functions of Real

Numbers • Periodic Functions • The 16-Point Unit Circle

4.4 Graphs of Sine and Cosine: Sinusoids 367

The Basic Waves Revisited • Sinusoids and Transformations

• Modeling Periodic Behavior with Sinusoids

4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 378

The Tangent Function • The Cotangent Function • The Secant Function

• The Cosecant Function

4.6 Graphs of Composite Trigonometric Functions 386

Combining Trigonometric and Algebraic Functions • Sums and Differences of Sinusoids

• Damped Oscillation

4.7 Inverse Trigonometric Functions 395

Inverse Sine Function • Inverse Cosine and Tangent Functions •

Composing Trigonometric and Inverse Trigonometric Functions •

Applications of Inverse Trigonometric Functions

4.8 Solving Problems with Trigonometry 405

More Right Triangle Problems • Simple Harmonic Motion

Key Ideas 416

Review Exercises 416

Modeling Project 419

CHAPTER 5 Analytic Trigonometry

5.1 Fundamental Identities 421

Identities • Basic Trigonometric Identities • Pythagorean Identities •

Cofunction Identities • Odd-Even Identities • Simplifying Trigonometric

Expressions • Solving Trigonometric Equations

5.2 Proving Trigonometric Identities 430

A Proof Strategy • Proving Identities • Disproving Non-Identities • Identities in Calculus

5.3 Sum and Difference Identities 438

Cosine of a Difference • Cosine of a Sum • Sine of a Sum or Difference •

Tangent of a Sum or Difference • Verifying a Sinusoid Algebraically

5.4 Multiple-Angle Identities 445

Double-Angle Identities • Power-Reducing Identities

• Half-Angle Identities Solving Trigonometric Equations

5.5 The Law of Sines 451

Deriving the Law of Sines • Solving Triangles (AAS, ASA) • The Ambiguous Case (SSA)

• Applications

5.6 The Law of Cosines 459

Deriving the Law of Cosines • Solving Triangles (SAS, SSS) • Triangle Area

and Heron’s Formula • Applications

Key Ideas 467

Review Exercises 467

Modeling Project 470

CHAPTER 6 Applications of Trigonometry

6.1 Vectors in the Plane 472

Two-Dimensional Vectors • Vector Operations • Unit Vectors • Direction Angles

• Applications of Vectors

6.2 Dot Product of Vectors 483

The Dot Product • Angle Between Vectors • Projecting One Vector onto Another • Work

6.3 Parametric Equations and Motion 491

Parametric Equations • Parametric Curves • Eliminating the Parameter •

Lines and Line Segments • Simulating Motion with a Grapher

6.4 Polar Coordinates 503

Polar Coordinate System • Coordinate Conversion • Equation Conversion

Finding Distance Using Polar Coordinates

6.5 Graphs of Polar Equations 510

Polar Curves and Parametric Curves • Symmetry • Analyzing Polar Graphs

Rose Curves • Limaçon Curves • Other Polar Curves

6.6 De Moivre’s Theorem and nth Roots 519

The Complex Plane • Polar Form of Complex Numbers • Multiplication and

Division of Complex Numbers • Powers of Complex Numbers • Roots of

Complex Numbers

Key Ideas 529

Review Exercises 530

Modeling Project 533

CHAPTER 7 Systems and Matrices

7.1 Solving Systems of Two Equations 535

Method of Substitution • Solving Systems Graphically • Method of Elimination • Applications

7.2 Matrix Algebra 545

Matrices • Matrix Addition and Subtraction • Matrix Multiplication • Identity

and Inverse Matrices • Determinant of a Square Matrix • Applications

7.3 Multivariate Linear Systems and Row Operations 559

Triangular Form for Linear Systems • Gaussian Elimination • Elementary

Row Operations and Row Echelon Form • Reduced Row Echelon Form •

Solving Systems Using Inverse Matrices • Partial Fraction Decomposition •

Other Applications

7.4 Systems of Inequalities in Two Variables 573

Graph of an Inequality • Systems of Inequalities • Linear Programming

Key Ideas 581

Review Exercises 581

Modeling Project 585

CHAPTER 8 Analytic Geometry in Two and Three Dimensions

8.1 Conic Sections and a New Look at Parabolas 587

Conic Sections • Geometry of a Parabola • Translations of Parabolas

• Reflective Property of a Parabola

8.2 Circles and Ellipses 598

Transforming the Unit Circle • Geometry of an Ellipse • Translations of

Ellipses • Orbits and Eccentricity • Reflective Property of an Ellipse

8.3 Hyperbolas 609

Geometry of a Hyperbola • Translations of Hyperbolas •

Eccentricity and Orbits • Reflective Property of a Hyperbola • Long-Range Navigation

8.4 Quadratic Equations with xy Terms 619

Quadratic Equations Revisited • Axis Rotation Formulas • Discriminant Test

8.5 Polar Equations of Conics 628

Eccentricity Revisited • Writing Polar Equations for Conics • Analyzing

Polar Equations of Conics • Orbits Revisited

8.6 Three-Dimensional Cartesian Coordinate System 637

Three-Dimensional Cartesian Coordinates • Distance and Midpoint

Formulas • Equation of a Sphere • Planes and Other Surfaces • Vectors in

Space • Lines in Space

Key Ideas 645

Review Exercises 646

Modeling Project 648

CHAPTER 9 Discrete Mathematics

9.1 Basic Combinatorics 650

Discrete Versus Continuous • The Importance of Counting • The

Multiplication Principle of Counting • Permutations • Combinations • Subsets of an n-Set

9.2 Binomial Theorem 660

Powers of Binomials • Pascal’s Triangle • Binomial Theorem • Factorial Identities

9.3 Sequences 666

Infinite Sequences • Limits of Infinite Sequences • Arithmetic and

Geometric Sequences • Sequences and Technology

9.4 Series 674

Summation Notation • Sums of Arithmetic and Geometric Sequences •

Infinite Series • Convergence of Geometric Series

9.5 Mathematical Induction 683

Tower of Hanoi Problem • Principle of Mathematical Induction • Induction and Deduction

Key Ideas 689

Review Exercises 689

Modeling Project 691

CHAPTER 10 Statistics and Probability

10.1 Probability 693

Sample Spaces and Probability Functions • Determining Probabilities •

Venn Diagrams • Tree Diagrams • Conditional Probability

10.2 Statistics (Graphical) 707

Statistics • Categorical Data • Quantitative Data: Stemplots • Frequency Tables • Histograms

• Describing Distributions: Shape • Time Plots

10.3 Statistics (Numerical) 720

Parameters and Statistics • Describing and Comparing Distributions •

Five-Number Summary • Boxplots • The Mean (and When to Use It) •

Variance and Standard Deviation • Normal Distributions

10.4 Random Variables and Probability Models 733

Probability Models and Expected Values • Binomial Probability Models •

Normal Model • Normal Approximation for Binomial Distributions

10.5 Statistical Literacy 748

Uses and Misuses of Statistics • Correlation Revisited • Importance

of Randomness • Samples, Surveys, and Observational Studies •

Experimental Design • Using Randomness • Simulations

Key Ideas 763

Review Exercises 763

Modeling Project 768

CHAPTER 11 An Introduction to Calculus: Limits, Derivatives, and Integrals

11.1 Limits and Motion: The Tangent Problem 770

Average Velocity • Instantaneous Velocity • Limits Revisited • The Connection to Tangent Lines

• The Derivative

11.2 Limits and Motion: The Area Problem 781

Distance from a Constant Velocity • Distance from a Changing Velocity •

Limits at Infinity • Connection to Areas • The Definite Integral

11.3 More on Limits 789

A Little History • Defining a Limit Informally • Properties of Limits • Limits

of Continuous Functions • One-Sided and Two-Sided Limits • Limits Involving Infinity

11.4 Numerical Derivatives and Integrals 800

Derivatives on a Calculator • Definite Integrals on a Calculator • Computing

a Derivative from Data • Computing a Definite Integral from Data

Key Ideas 809

Review Exercises 809

Modeling Project 810

APPENDIX A Algebra Review

A.1 Radicals and Rational Exponents 811

Radicals • Simplifying Radical Expressions • Rationalizing the Denominator

• Rational Exponents

A.2 Polynomials and Factoring 816

Adding, Subtracting, and Multiplying Polynomials • Special Products •

Factoring Polynomials Using Special Products • Factoring Trinomials • Factoring by Grouping

A.3 Fractional Expressions 823

Algebraic Expressions and Their Domains • Reducing Rational Expressions

Operations with Rational Expressions • Compound Rational Expressions

APPENDIX B Logic

B.1 Logic: An Introduction 828

Statements • Compound Statements

B.2 Conditionals and Biconditionals 834

Forms of Statements • Valid Reasoning

APPENDIX C Key Formulas

C.1 Formulas from Algebra 841

C.2 Formulas from Geometry 842

C.3 Formulas from Trigonometry 842

C.4 Formulas from Analytic Geometry 844

C.5 Gallery of Basic Functions 845

Bibliography 846

Glossary 847

Selected Answers 865

Credits 945

Applications Index 947

Index 950