College Algebra, 11e Michael Sullivan ( )

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 Gr ...

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