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• To the Student
• Prepare for Class “Read the Book”
• Practice “Work the Problems”
• Review “Study for Quizzes and Tests”
• Dedication
• Title Page
• Copyright
• Contents
• Three Distinct Series
• The Flagship Series
• Preface to the Instructor
• Get the Most Out of MyLab Math
• Resources for Success
• Applications Index
• Chapter 1. Graphs
• 1.1 The Distance and Midpoint Formulas
• Use the Distance Formula
• Use the Midpoint Formula
• 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
• Graph Equations by Plotting Points
• Find Intercepts from a Graph
• Find Intercepts from an Equation
• Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin
• Know How to Graph Key Equations
• 1.3 Lines
• Calculate and Interpret the Slope of a Line
• Graph Lines Given a Point and the Slope
• Find the Equation of a Vertical Line
• Use the Point-Slope Form of a Line; Identify Horizontal Lines
• Use the Slope-Intercept Form of a Line
• Find the Equation of a Line Given Two Points
• Graph Lines Written in General Form Using Intercepts
• Find Equations of Parallel Lines
• Find Equations of Perpendicular Lines
• 1.4 Circles
• Write the Standard Form of the Equation of a Circle
• Graph a Circle
• Work with the General Form of the Equation of a Circle
• Chapter Review
• Chapter Test
• Chapter Project
• Chapter 2. Functions and Their Graphs
• 2.1 Functions
• Describe a Relation
• Determine Whether a Relation Represents a Function
• Use Function Notation; Find the Value of a Function
• Find the Difference Quotient of a Function
• Find the Domain of a Function Defined by an Equation
• Form the Sum, Difference, Product, and Quotient of Two Functions
• 2.2 The Graph of a Function
• Identify the Graph of a Function
• Obtain Information from or about the Graph of a Function
• 2.3 Properties of Functions
• Identify Even and Odd Functions from a Graph
• Identify Even and Odd Functions from an Equation
• Use a Graph to Determine Where a Function is Increasing, Decreasing, or Constant
• Use a Graph to Locate Local Maxima and Local Minima
• Use a Graph to Locate the Absolute Maximum and the Absolute Minimum
• Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Functio
• Find the Average Rate of Change of a Function
• 2.4 Library of Functions; Piecewise-defined Functions
• Graph the Functions Listed in the Library of Functions
• Analyze a Piecewise-defined Function
• 2.5 Graphing Techniques: Transformations
• Graph Functions Using Vertical and Horizontal Shifts
• Graph Functions Using Compressions and Stretches
• Graph Functions Using Reflections about the x-Axis and the y-Axis
• 2.6 Mathematical Models: Building Functions
• Build and Analyze Functions
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 3. Linear and Quadratic Functions
• 3.1 Properties of Linear Functions and Linear Models
• Graph Linear Functions
• Use Average Rate of Change to Identify Linear Functions
• Determine Whether a Linear Function Is Increasing, Decreasing, or Constant
• Build Linear Models from Verbal Descriptions
• 3.2 Building Linear Models from Data
• Draw and Interpret Scatter Plots
• Distinguish between Linear and Nonlinear Relations
• Use a Graphing Utility to Find the Line of Best Fit
• 3.3 Quadratic Functions and Their Properties
• Graph a Quadratic Function Using Transformations
• Identify the Vertex and Axis of Symmetry of a Parabola
• Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts
• Find a Quadratic Function Given Its Vertex and One Other Point
• Find the Maximum or Minimum Value of a Quadratic Function
• 3.4 Building Quadratic Models from Verbal Descriptions and from Data
• Build Quadratic Models from Verbal Descriptions
• Build Quadratic Models from Data
• 3.5 Inequalities Involving Quadratic Functions
• Solve Inequalities Involving a Quadratic Function
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 4. Polynomial and Rational Functions
• 4.1 Polynomial Functions
• Identify Polynomial Functions and Their Degree
• Graph Polynomial Functions Using Transformations
• Identify the Real Zeros of a Polynomial Function and Their Multiplicity
• 4.2 Graphing Polynomial Functions; Models
• Graph a Polynomial Function
• Graph a Polynomial Function Using a Graphing Utility
• Build Cubic Models from Data
• 4.3 Properties of Rational Functions
• Find the Domain of a Rational Function
• Find the Vertical Asymptotes of a Rational Function
• Find a Horizontal or an Oblique Asymptote of a Rational Function
• 4.4 The Graph of a Rational Function
• Graph a Rational Function
• Solve Applied Problems Involving Rational Functions
• 4.5 Polynomial and Rational Inequalities
• Solve Polynomial Inequalities
• Solve Rational Inequalities
• 4.6 The Real Zeros of a Polynomial Function
• Use the Remainder and Factor Theorems
• Use Descartes’ Rule of Signs to Determine the Number of Positive and the Number of Negative Real Z
• Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function
• Find the Real Zeros of a Polynomial Function
• Solve Polynomial Equations
• Use the Theorem for Bounds on Zeros
• Use the Intermediate Value Theorem
• 4.7 Complex Zeros; Fundamental Theorem of Algebra
• Use the Conjugate Pairs Theorem
• Find a Polynomial Function with Specified Zeros
• Find the Complex Zeros of a Polynomial Function
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 5. Exponential and Logarithmic Functions
• 5.1 Composite Functions
• Form a Composite Function
• Find the Domain of a Composite Function
• 5.2 One-to-One Functions; Inverse Functions
• Determine Whether a Function Is One-to-One
• Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function
• Verify an Inverse Function
• Find the Inverse of a Function Defined by an Equation
• 5.3 Exponential Functions
• Evaluate Exponential Functions
• Graph Exponential Functions
• Define the Number e
• Solve Exponential Equations
• 5.4 Logarithmic Functions
• Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential St
• Evaluate Logarithmic Expressions
• Determine the Domain of a Logarithmic Function
• Graph Logarithmic Functions
• Solve Logarithmic Equations
• 5.5 Properties of Logarithms
• Work with the Properties of Logarithms
• Write a Logarithmic Expression as a Sum or Difference of Logarithms
• Write a Logarithmic Expression as a Single Logarithm
• Evaluate Logarithms Whose Base Is Neither 10 Nor e
• 5.6 Logarithmic and Exponential Equations
• Solve Logarithmic Equations
• Solve Exponential Equations
• Solve Logarithmic and Exponential Equations Using a Graphing Utility
• 5.7 Financial Models
• Determine the Future Value of a Lump Sum of Money
• Calculate Effective Rates of Return
• Determine the Present Value of a Lump Sum of Money
• Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money
• 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
• Model Populations That Obey the Law of Uninhibited Growth
• Model Populations That Obey the Law of Uninhibited Decay
• Use Newton’s Law of Cooling
• Use Logistic Models
• 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
• Build an Exponential Model from Data
• Build a Logarithmic Model from Data
• Build a Logistic Model from Data
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 6. Trigonometric Functions
• 6.1 Angles, Arc Length, and Circular Motion
• Angles and Degree Measure
• Convert between Decimal and Degree, Minute, Second Measures for Angles
• Find the Length of an Arc of a Circle
• Convert from Degrees to Radians and from Radians to Degrees
• Find the Area of a Sector of a Circle
• Find the Linear Speed of an Object Traveling in Circular Motion
• 6.2 Trigonometric Functions: Unit Circle Approach
• Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle
• Find the Exact Values of the Trigonometric Functions of Quadrantal Angles
• Find the Exact Values of the Trigonometric Functions of π/4 = 45°
• Find the Exact Values of the Trigonometric Functions of π/6 = 30° and π/3 = 60°
• Find the Exact Values of the Trigonometric Functions for Integer Multiples of π/6 = 30°, π/4 = 45
• Use a Calculator to Approximate the Value of a Trigonometric Function
• Use a Circle of Radius r to Evaluate the Trigonometric Functions
• 6.3 Properties of the Trigonometric Functions
• Determine the Domain and the Range of the Trigonometric Functions
• Determine the Period of the Trigonometric Functions
• Determine the Signs of the Trigonometric Functions in a Given Quadrant
• Find the Values of the Trigonometric Functions Using Fundamental Identities
• Find the Exact Values of the Trigonometric Functions of an Angle Given One of the Functions and the
• Use Even-Odd Properties to Find the Exact Values of the Trigonometric Functions
• 6.4 Graphs of the Sine and Cosine Functions
• Graph the Sine Function y = sin x and Functions of the Form y = A sin (ωx)
• Graph the Cosine Function y = cos x and Functions of the Form y = A cos (ωx)
• Determine the Amplitude and Period of Sinusoidal Functions
• Graph Sinusoidal Functions Using Key Points
• Find an Equation for a Sinusoidal Graph
• 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
• Graph the Tangent Function y = tan x and the Cotangent Function y = cot x
• Graph Functions of the Form y = A tan (ωx) + B and y = A cot (ωx) + B
• Graph the Cosecant Function y = csc x and the Secant Function y = sec x
• Graph Functions of the Form y = A csc (ωx) + B and y = A sec (ωx) + B
• 6.6 Phase Shift; Sinusoidal Curve Fitting
• Graph Sinusoidal Functions of the Form y = A sin (ωx – ϕ) + B
• Build Sinusoidal Models from Data
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 7. Analytic Trigonometry
• 7.1 The Inverse Sine, Cosine, and Tangent Functions
• Define the Inverse Sine Function
• Find the Value of an Inverse Sine Function
• Define the Inverse Cosine Function
• Find the Value of an Inverse Cosine Function
• Define the Inverse Tangent Function
• Find the Value of an Inverse Tangent Function
• Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions
• Find the Inverse Function of a Trigonometric Function
• Solve Equations Involving Inverse Trigonometric Functions
• 7.2 The Inverse Trigonometric Functions (Continued)
• Define the Inverse Secant, Cosecant, and Cotangent Functions
• Find the Value of Inverse Secant, Cosecant, and Cotangent Functions
• Find the Exact Value of Composite Functions Involving the Inverse Trigonometric Functions
• Write a Trigonometric Expression as an Algebraic Expression
• 7.3 Trigonometric Equations
• Solve Equations Involving a Single Trigonometric Function
• Solve Trigonometric Equations Using a Calculator
• Solve Trigonometric Equations Quadratic in Form
• Solve Trigonometric Equations Using Fundamental Identities
• Solve Trigonometric Equations Using a Graphing Utility
• 7.4 Trigonometric Identities
• Use Algebra to Simplify Trigonometric Expressions
• Establish Identities
• 7.5 Sum and Difference Formulas
• Use Sum and Difference Formulas to Find Exact Values
• Use Sum and Difference Formulas to Establish Identities
• Use Sum and Difference Formulas Involving Inverse Trigonometric Functions
• Solve Trigonometric Equations Linear in Sine and Cosine
• 7.6 Double-angle and Half-angle Formulas
• Use Double-angle Formulas to Find Exact Values
• Use Double-angle Formulas to Establish Identities
• Use Half-angle Formulas to Find Exact Values
• 7.7 Product-to-Sum and Sum-to-Product Formulas
• Express Products as Sums
• Express Sums as Products
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 8. Applications of Trigonometric Functions
• 8.1 Right Triangle Trigonometry; Applications
• Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles
• Use the Complementary Angle Theorem
• Solve Right Triangles
• Solve Applied Problems
• 8.2 The Law of Sines
• Solve SAA or ASA Triangles
• Solve SSA Triangles
• Solve Applied Problems
• 8.3 The Law of Cosines
• Solve SAS Triangles
• Solve SSS Triangles
• Solve Applied Problems
• 8.4 Area of a Triangle
• Find the Area of SAS Triangles
• Find the Area of SSS Triangles
• 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
• Build a Model for an Object in Simple Harmonic Motion
• Analyze Simple Harmonic Motion
• Analyze an Object in Damped Motion
• Graph the Sum of Two Functions
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 9. Polar Coordinates; Vectors
• 9.1 Polar Coordinates
• Plot Points Using Polar Coordinates
• Convert from Polar Coordinates to Rectangular Coordinates
• Convert from Rectangular Coordinates to Polar Coordinates
• Transform Equations between Polar and Rectangular Forms
• 9.2 Polar Equations and Graphs
• Identify and Graph Polar Equations by Converting to Rectangular Equations
• Test Polar Equations for Symmetry
• Graph Polar Equations by Plotting Points
• 9.3 The Complex Plane; De Moivre’s Theorem
• Plot Points in the Complex Plane
• Convert a Complex Number between Rectangular Form and Polar Form or Exponential Form
• Find Products and Quotients of Complex Numbers
• Use De Moivre’s Theorem
• Find Complex Roots
• 9.4 Vectors
• Graph Vectors
• Find a Position Vector
• Add and Subtract Vectors Algebraically
• Find a Scalar Multiple and the Magnitude of a Vector
• Find a Unit Vector
• Find a Vector from Its Direction and Magnitude
• Model with Vectors
• 9.5 The Dot Product
• Find the Dot Product of Two Vectors
• Find the Angle between Two Vectors
• Determine Whether Two Vectors Are Parallel
• Determine Whether Two Vectors Are Orthogonal
• Decompose a Vector into Two Orthogonal Vectors
• Compute Work
• 9.6 Vectors in Space
• Find the Distance between Two Points in Space
• Find Position Vectors in Space
• Perform Operations on Vectors
• Find the Dot Product
• Find the Angle between Two Vectors
• Find the Direction Angles of a Vector
• 9.7 The Cross Product
• Find the Cross Product of Two Vectors
• Know Algebraic Properties of the Cross Product
• Know Geometric Properties of the Cross Product
• Find a Vector Orthogonal to Two Given Vectors
• Find the Area of a Parallelogram
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 10. Analytic Geometry
• 10.1 Conics
• Know the Names of the Conics
• 10.2 The Parabola
• Analyze Parabolas with Vertex at the Origin
• Analyze Parabolas with Vertex at (h, k)
• Solve Applied Problems Involving Parabolas
• 10.3 The Ellipse
• Analyze Ellipses with Center at the Origin
• Analyze Ellipses with Center at (h, k)
• Solve Applied Problems Involving Ellipses
• 10.4 The Hyperbola
• Analyze Hyperbolas with Center at the Origin
• Find the Asymptotes of a Hyperbola
• Analyze Hyperbolas with Center at (h, k)
• Solve Applied Problems Involving Hyperbolas
• 10.5 Rotation of Axes; General Form of a Conic
• Identify a Conic
• Use a Rotation of Axes to Transform Equations
• Analyze an Equation Using a Rotation of Axes
• Identify Conics without Rotating the Axes
• 10.6 Polar Equations of Conics
• Analyze and Graph Polar Equations of Conics
• Convert the Polar Equation of a Conic to a Rectangular Equation
• 10.7 Plane Curves and Parametric Equations
• Graph Parametric Equations
• Find a Rectangular Equation for a Plane Curve Defined Parametrically
• Use Time as a Parameter in Parametric Equations
• Find Parametric Equations for Plane Curves Defined by Rectangular Equations
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 11. Systems of Equations and Inequalities
• 11.1 Systems of Linear Equations: Substitution and Elimination
• Solve Systems of Equations by Substitution
• Solve Systems of Equations by Elimination
• Identify Inconsistent Systems of Equations Containing Two Variables
• Express the Solution of a System of Dependent Equations Containing Two Variables
• Solve Systems of Three Equations Containing Three Variables
• Identify Inconsistent Systems of Equations Containing Three Variables
• Express the Solution of a System of Dependent Equations Containing Three Variables
• 11.2 Systems of Linear Equations: Matrices
• Write the Augmented Matrix of a System of Linear Equations
• Write the System of Equations from the Augmented Matrix
• Perform Row Operations on a Matrix
• Solve a System of Linear Equations Using Matrices
• 11.3 Systems of Linear Equations: Determinants
• Evaluate 2 by 2 Determinants
• Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables
• Evaluate 3 by 3 Determinants
• Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables
• Know Properties of Determinants
• 11.4 Matrix Algebra
• Find the Sum and Difference of Two Matrices
• Find Scalar Multiples of a Matrix
• Find the Product of Two Matrices
• Find the Inverse of a Matrix
• Solve a System of Linear Equations Using an Inverse Matrix
• 11.5 Partial Fraction Decomposition
• Decompose P/Q Where Q Has Only Nonrepeated Linear Factors
• Decompose P/Q Where Q Has Repeated Linear Factors
• Decompose P/Q Where Q Has a Nonrepeated Irreducible Quadratic Factor
• Decompose P/Q Where Q Has a Repeated Irreducible Quadratic Factor
• 11.6 Systems of Nonlinear Equations
• Solve a System of Nonlinear Equations Using Substitution
• Solve a System of Nonlinear Equations Using Elimination
• 11.7 Systems of Inequalities
• Graph an Inequality
• Graph a System of Inequalities
• 11.8 Linear Programming
• Set Up a Linear Programming Problem
• Solve a Linear Programming Problem
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 12. Sequences; Induction; the Binomial Theorem
• 12.1 Sequences
• List the First Several Terms of a Sequence
• List the Terms of a Sequence Defined by a Recursive Formula
• Use Summation Notation
• Find the Sum of a Sequence
• 12.2 Arithmetic Sequences
• Determine Whether a Sequence Is Arithmetic
• Find a Formula for an Arithmetic Sequence
• Find the Sum of an Arithmetic Sequence
• 12.3 Geometric Sequences; Geometric Series
• Determine Whether a Sequence Is Geometric
• Find a Formula for a Geometric Sequence
• Find the Sum of a Geometric Sequence
• Determine Whether a Geometric Series Converges or Diverges
• Solve Annuity Problems
• 12.4 Mathematical Induction
• Prove Statements Using Mathematical Induction
• 12.5 The Binomial Theorem
• Evaluate (n/j)
• Use the Binomial Theorem
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 13. Counting and Probability
• 13.1 Counting
• Find All the Subsets of a Set
• Count the Number of Elements in a Set
• Solve Counting Problems Using the Multiplication Principle
• 13.2 Permutations and Combinations
• Solve Counting Problems Using Permutations Involving n Distinct Objects
• Solve Counting Problems Using Combinations
• Solve Counting Problems Using Permutations Involving n Nondistinct Objects
• 13.3 Probability
• Construct Probability Models
• Compute Probabilities of Equally Likely Outcomes
• Find Probabilities of the Union of Two Events
• Use the Complement Rule to Find Probabilities
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects
• Chapter 14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
• 14.1 Investigating Limits Using Tables and Graphs
• Investigate a Limit Using a Table
• Investigate a Limit Using a Graph
• 14.2 Algebraic Techniques for Finding Limits
• Find the Limit of a Sum, a Difference, and a Product
• Find the Limit of a Polynomial
• Find the Limit of a Power or a Root
• Find the Limit of a Quotient
• Find the Limit of an Average Rate of Change
• 14.3 One-sided Limits; Continuity
• Find the One-sided Limits of a Function
• Determine Whether a Function Is Continuous at a Number
• 14.4 The Tangent Problem; The Derivative
• Find an Equation of the Tangent Line to the Graph of a Function
• Find the Derivative of a Function
• Find Instantaneous Rates of Change
• Find the Instantaneous Velocity of an Object
• 14.5 The Area Problem; The Integral
• Approximate the Area under the Graph of a Function
• Approximate Integrals Using a Graphing Utility
• Chapter Review
• Chapter Test
• Chapter Projects
• Appendix A. Review
• A.1 Algebra Essentials
• Work with Sets
• Graph Inequalities
• Find Distance on the Real Number Line
• Evaluate Algebraic Expressions
• Determine the Domain of a Variable
• Use the Laws of Exponents
• Evaluate Square Roots
• Use a Calculator to Evaluate Exponents
• A.2 Geometry Essentials
• Use the Pythagorean Theorem and Its Converse
• Know Geometry Formulas
• Understand Congruent Triangles and Similar Triangles
• A.3 Polynomials
• Recognize Monomials
• Recognize Polynomials
• Know Formulas for Special Products
• Divide Polynomials Using Long Division
• Factor Polynomials
• Complete the Square
• A.4 Synthetic Division
• Divide Polynomials Using Synthetic Division
• A.5 Rational Expressions
• Reduce a Rational Expression to Lowest Terms
• Multiply and Divide Rational Expressions
• Add and Subtract Rational Expressions
• Use the Least Common Multiple Method
• Simplify Complex Rational Expressions
• A.6 Solving Equations
• Solve Equations by Factoring
• Solve Equations Involving Absolute Value
• Solve a Quadratic Equation by Factoring
• Solve a Quadratic Equation by Completing the Square
• Solve a Quadratic Equation Using the Quadratic Formula
• A.7 Complex Numbers; Quadratic Equations in the Complex Number System
• Add, Subtract, Multiply, and Divide Complex Numbers
• Solve Quadratic Equations in the Complex Number System
• A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
• Translate Verbal Descriptions into Mathematical Expressions
• Solve Interest Problems
• Solve Mixture Problems
• Solve Uniform Motion Problems
• Solve Constant Rate Job Problems
• A.9 Interval Notation; Solving Inequalities
• Use Interval Notation
• Use Properties of Inequalities
• Solve Inequalities
• Solve Combined Inequalities
• Solve Inequalities Involving Absolute Value
• A.10 nth Roots; Rational Exponents
• Work with nth Roots
• Simplify Radicals
• Rationalize Denominators and Numerators
• Solve Radical Equations
• Simplify Expressions with Rational Exponents
• Appendix B. Graphing Utilities
• B.1 The Viewing Rectangle
• B.2 Using a Graphing Utility to Graph Equations
• B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
• B.4 Using a Graphing Utility to Solve Equations
• B.5 Square Screens
• B.6 Using a Graphing Utility to Graph Inequalities
• B.7 Using a Graphing Utility to Solve Systems of Linear Equations
• B.8 Using a Graphing Utility to Graph a Polar Equation
• B.9 Using a Graphing Utility to Graph Parametric Equations
• Answers
• Photo Credits
• Subject Index