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