College Algebra 7th Edition by Robert Blitzer eBook [PDF]

College Algebra 7th Edition by Robert Blitzer eBook [PDF] COLLEGE ALGEBRA COLLEGE ALGEBRA CONTENTS PREFACE What’s New in the Seventh Edition? What Content and Organizational Changes Have Been Made to the Seventh Ed ...

College Algebra 7th Edition by Robert Blitzer eBook [PDF] COLLEGE ALGEBRA COLLEGE ALGEBRA CONTENTS PREFACE What’s New in the Seventh Edition? What Content and Organizational Changes Have Been Made to the Seventh Edition? What Familiar Features Have Been Retained in the Seventh Edition? Get the Most Out of MyMathLab® MyMathLab Online Course for College Algebra by Robert Blitzer (access code required) Resources for Success TO THE STUDENT ABOUT THE AUTHOR APPLICATIONS INDEX A B C D E F G H I J K L M N O P R S T U V W X CHAPTER P Prerequisites: Fundamental Concepts of Algebra Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers What am I Supposed to learn? Algebraic Expressions Evaluating Algebraic Expressions Formulas and Mathematical Models Sets The Set of Real Numbers The Real Number Line Ordering the Real Numbers Absolute Value Properties of Real Numbers and Algebraic Expressions Simplifying Algebraic Expressions Properties of Negatives SOLUTION Check Point 9 CONCEPT AND VOCABULARY CHECK EXERCISE SET P.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Preview Exercises Section P.2 Exponents and Scientific Notation What am I Supposed to learn? The Product and Quotient Rules Zero as an Exponent Negative Integers as Exponents The Power Rule for Exponents (Powers to Powers) The Products-to-Powers Rule for Exponents The Quotients-to-Powers Rule for Exponents Simplifying Exponential Expressions Scientific Notation Converting from Scientific to Decimal Notation SOLUTION Check Point 8 Converting from Decimal to Scientific Notation SOLUTION Check Point 9 SOLUTION Check Point 10 Computations with Scientific Notation SOLUTION Check Point 11 Applications: Putting Numbers in Perspective SOLUTION Check Point 12 CONCEPT AND VOCABULARY CHECK EXERCISE SET P.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Group Exercise Preview Exercises Section P.3 Radicals and Rational Exponents What am I Supposed to learn? Square Roots Simplifying Expressions of the Form a2 The Product Rule for Square Roots The Quotient Rule for Square Roots Adding and Subtracting Square Roots Rationalizing Denominators Other kinds of Roots The Product and Quotient Rules for Other Roots SOLUTION Check Point 8 SOLUTION Check Point 9 Rational Exponents CONCEPT AND VOCABULARY CHECK EXERCISE SET P.3 Practice Exercises Practice Plus Application Exercises Writing in Mathematics Critical Thinking Exercises Preview Exercises Section P.4 Polynomials What am I Supposed to learn? How We Define Polynomials How We Describe Polynomials Adding and Subtracting Polynomials Multiplying Polynomials The Product of Two Binomials: FOIL Multiplying the Sum and Difference of Two Terms The Square of a Binomial SOLUTION Check Point 5 SOLUTION Check Point 6 Special Products Polynomials in Several Variables CONCEPT AND VOCABULARY CHECK EXERCISE SET P.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Preview Exercises CHAPTER P Mid-Chapter Check Point Section P.5 Factoring Polynomials What am I Supposed to learn? Common Factors Factoring by Grouping Factoring Trinomials Factoring the Difference of Two Squares Factoring Perfect Square Trinomials Factoring the Sum or Difference of Two Cubes A Strategy for Factoring Polynomials Factoring Algebraic Expressions Containing Fractional and Negative Exponents CONCEPT AND VOCABULARY CHECK EXERCISE SET P.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Preview Exercises Section P.6 Rational Expressions What am I Supposed to learn? Rational Expressions Simplifying Rational Expressions Multiplying Rational Expressions Dividing Rational Expressions Adding and Subtracting Rational Expressions with the Same Denominator Adding and Subtracting Rational Expressions with Different Denominators SOLUTION Check Point 6 SOLUTION Check Point 7 SOLUTION Check Point 8 SOLUTION Check Point 9 Complex Rational Expressions CONCEPT AND VOCABULARY CHECK EXERCISE SET P.6 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Preview Exercises CHAPTER P Summary, Review, and Test SUMMARY: BASIC FORMULAS REVIEW EXERCISES P.1 P.2 P.3 P.4 P.5 P.6 CHAPTER P TEST CHAPTER 1 Equations and Inequalities Section 1.1 Graphs and Graphing Utilities What am I Supposed to learn? Points and Ordered Pairs Graphs of Equations Graphing Equations and Creating Tables Using a Graphing Utility Intercepts Interpreting Information Given by Graphs CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Preview Exercises Section 1.2 Linear Equations and Rational Equations What am I Supposed to learn? Solving Linear Equations in One Variable Linear Equations with Fractions Rational Equations Types of Equations Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Preview Exercises Section 1.3 Models and applications What am I Supposed to learn? Problem Solving with Linear Equations Solving a Formula for One of Its Variables CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.3 Practice and Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Preview Exercises Section 1.4 Complex numbers What am I Supposed to learn? The Imaginary Unit i Operations with Complex Numbers Complex Conjugates and division Roots of Negative Numbers CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Critical Thinking Exercises Preview Exercises Section 1.5 Quadratic Equations What am I Supposed to learn? Solving Quadratic Equations by Factoring Solving Quadratic Equations by the Square Root Property Completing the Square Solving Quadratic Equations Using the Quadratic Formula The Discriminant Determining Which Method to Use Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Preview Exercises CHAPTER 1 Mid-Chapter Check Point Section 1.6 Other Types of Equations What am I Supposed to learn? Polynomial Equations Radical Equations Equations with Rational Exponents Equations That Are Quadratic in Form Equations Involving Absolute Value Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.6 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Preview Exercises Section 1.7 Linear Inequalities and Absolute Value Inequalities What am I Supposed to learn? Interval Notation Intersections and Unions of Intervals Solving Linear Inequalities in One Variable Inequalities with Unusual Solution Sets Solving Compound Inequalities Solving Inequalities with Absolute Value Applications SOLUTION Check Point 11 CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.7 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Preview Exercises CHAPTER 1 Summary, Review, and Test SUMMARY REVIEW EXERCISES 1.1 1.2 1.3 1.4 1.5 1.6 1.7 CHAPTER 1 TEST CHAPTER 2 Functions and Graphs Section 2.1 Basics of Functions and Their Graphs What am I Supposed to learn? Relations Functions Functions as Equations Function Notation Graphs of Functions The Vertical Line Test Obtaining Information from Graphs Identifying Domain and Range from a Function’s Graph Identifying Intercepts from a Function’s Graph CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 2.2 More on Functions and Their Graphs What am I Supposed to learn? Increasing and Decreasing Functions Relative Maxima and Relative Minima Tests for Symmetry Even and Odd Functions Piecewise Functions Functions and Difference Quotients CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 2.3 Linear Functions and slope What am I Supposed to learn? The slope of a Line The point-slope Form of the Equation of a Line The slope-Intercept Form of the Equation of a Line Equations of Horizontal and Vertical Lines The General Form of the Equation of a Line Using Intercepts to Graph Ax+By+C=0 Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 2.4 More on slope What am I Supposed to learn? Parallel and Perpendicular Lines Slope as Rate of Change The Average Rate of Change of a Function CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 2 Mid-Chapter Check Point Section 2.5 Transformations of Functions What am I Supposed to learn? Graphs of Common Functions Vertical shifts Horizontal Shifts Reflections of Graphs Vertical stretching and shrinking Horizontal Stretching and Shrinking Sequences of Transformations CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 2.6 Combinations of Functions; Composite Functions What am I Supposed to learn? The Domain of a Function The Algebra of Functions Composite Functions Decomposing Functions CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.6 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 2.7 Inverse Functions What am I Supposed to learn? Inverse Functions Finding the inverse of a Function The horizontal line Test and One-to-One Functions Graphs of f and f−1 CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.7 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 2.8 Distance and Midpoint Formulas; Circles What am I Supposed to learn? The Distance Formula The Midpoint Formula Circles CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.8 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 2 Summary, Review, and Test SUMMARY REVIEW EXERCISES 2.1 and 2.2 2.3 and 2.4 2.5 2.6 2.7 2.8 CHAPTER 2 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–2) CHAPTER 3 Polynomial and Rational Functions Section 3.1 Quadratic Functions What am I supposed to learn? Graphs of Quadratic Functions Graphing Quadratic Functions in Standard Form Graphing Quadratic Functions in the Form f(x)=ax2+bx+c SOLUTION Check Point 3 Minimum and Maximum Values of Quadratic Functions Applications of Quadratic Functions CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 3.2 Polynomial Functions and Their Graphs What am I Supposed to learn? Smooth, Continuous Graphs End Behavior of Polynomial Functions Zeros of Polynomial Functions Multiplicities of Zeros The Intermediate Value Theorem Turning Points of Polynomial Functions A Strategy for Graphing Polynomial Functions CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 3.3 Dividing Polynomials; Remainder and Factor Theorems What am I Supposed to learn? Long Division of Polynomials and the Division Algorithm Dividing Polynomials Using Synthetic Division The Remainder Theorem The Factor Theorem CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 3.4 Zeros of Polynomial Functions What am I Supposed to learn? The Rational Zero Theorem The Fundamental Theorem of Algebra The Linear Factorization Theorem Descartes’s Rule of Signs CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 3 Mid-Chapter Check Point Section 3.5 Rational Functions and Their Graphs What am I Supposed to learn? Rational Functions Vertical Asymptotes of Rational Functions Horizontal Asymptotes of Rational Functions Using Transformations to Graph Rational Functions Graphing Rational Functions Slant Asymptotes Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 3.6 Polynomial and Rational Inequalities What am I Supposed to learn? Solving Polynomial Inequalities Solving Rational Inequalities Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.6 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 3.7 Modeling Using Variation What am I Supposed to learn? Direct Variation Inverse Variation Combined Variation Joint Variation CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.7 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 3 Summary, Review, and Test SUMMARY REVIEW EXERCISES 3.1 3.2 3.3 3.4 3.5 3.6 3.7 CHAPTER 3 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–3) CHAPTER 4 Exponential and Logarithmic Functions Section 4.1 Exponential Functions What am I Supposed to learn? Graphing Exponential Functions Transformations of Exponential Functions SOLUTION Check Point 4 SOLUTION Check Point 5 The Natural Base e Compound Interest CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 4.2 Logarithmic Functions What am I Supposed to learn? The Definition of Logarithmic Functions Basic Logarithmic Properties Graphs of Logarithmic Functions The Domain of a Logarithmic Function Common Logarithms Natural Logarithms CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 4.3 Properties of Logarithms What am I Supposed to learn? The Product Rule The Quotient Rule The Power Rule Expanding logarithmic Expressions Condensing Logarithmic Expressions The Change-of-Base property CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 4 Mid-Chapter Check Point Section 4.4 Exponential and Logarithmic Equations What am I Supposed to learn? Exponential Equations Logarithmic Equations Applications SOLUTION Check Point 9 SOLUTION Check Point 10 SOLUTION Check Point 11 CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 4.5 Exponential Growth and Decay; Modeling Data What am I Supposed to learn? Exponential Growth and Decay Logistic Growth Models Modeling Data Expressing y=abx in Base e CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.5 Practice Exercises and Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 4 Summary, Review, and Test SUMMARY REVIEW EXERCISES 4.1 4.2 4.3 4.4 4.5 CHAPTER 4 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–4) CHAPTER 5 Systems of Equations and Inequalities Section 5.1 Systems of Linear Equations in Two Variables What am I Supposed to learn? Systems of Linear Equations and Their Solutions Eliminating a Variable Using the Substitution Method Eliminating a Variable Using the Addition Method Linear Systems Having No Solution or Infinitely Many Solutions Functions of Business: Break-Even Analysis Problems Involving Mixtures SOLUTION Check Point 8 CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 5.2 Systems of Linear Equations in Three Variables What am I Supposed to learn? Systems of Linear Equations in Three Variables and Their Solutions Solving Systems of Linear Equations in Three Variables by Eliminating Variables Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 5.3 Partial Fractions What am I Supposed to learn? The Idea behind Partial Fraction Decomposition The Partial Fraction decomposition of a rational Expression with Distinct Linear Factors in the denominator The Partial Fraction Decomposition of a Rational Expression with Linear Factors in the denominator, Some of Which Are repeated The Partial Fraction Decomposition of a Rational Expression with Prime, Nonrepeated Quadratic Factors in the Denominator The Partial Fraction Decomposition of a Rational Expression with a Prime, repeated Quadratic Factor in the Denominator CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 5.4 Systems of Nonlinear Equations in Two Variables What am I Supposed to learn? Systems of Nonlinear Equations and Their Solutions Eliminating a Variable Using the Substitution Method Eliminating a Variable Using the Addition Method Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 5 Mid-Chapter Check Point Section 5.5 Systems of Inequalities What am I Supposed to learn? Linear Inequalities in Two Variables and Their Solutions The Graph of a Linear Inequality in Two Variables Graphing Linear Inequalities without Using Test Points SOLUTION Check Point 3 Graphing a Nonlinear Inequality in Two Variables Modeling with Systems of Linear Inequalities Graphing Systems of Linear Inequalities CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 5.6 Linear Programming What am I Supposed to learn? Objective Functions in Linear Programming Constraints in Linear Programming Solving Problems with Linear Programming CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.6 Practice Exercises Application Exercises Explaining the Concepts Critical Thinking Exercises Group Exercises Retaining the Concepts Preview Exercises CHAPTER 5 Summary, Review, and Test SUMMARY REVIEW EXERCISES 5.1 5.2 5.3 5.4 5.5 5.6 CHAPTER 5 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–5) CHAPTER 6 Matrices and Determinants Section 6.1 Matrix Solutions to Linear Systems What am I Supposed to learn? Augmented Matrices Matrix Row Operations Solving Linear Systems Using Gaussian Elimination Solving Linear Systems Using Gauss-Jordan Elimination TECHNOLOGY SOLUTION Check Point 5 CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 6.2 Inconsistent and Dependent Systems and Their Applications What am I Supposed to learn? Nonsquare Systems Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 6.3 Matrix Operations and Their Applications What am I Supposed to learn? Notations for Matrices Equality of Matrices Matrix Addition and Subtraction Scalar Multiplication Matrix Multiplication Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercise Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 6 Mid-Chapter Check Point Section 6.4 Multiplicative Inverses of Matrices and Matrix Equations What am I Supposed to learn? The Multiplicative Identity Matrix The Multiplicative Inverse of a Matrix A Quick Method for Finding the Multiplicative Inverse of a 2×2 Matrix SOLUTION Check Point 3 Finding Multiplicative Inverses of n×n Matrices with n Greater Than 2 SOLUTION Check Point 4 Solving Systems of Equations Using Multiplicative Inverses of Matrices Applications of Matrix Inverses to Coding CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.4 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 6.5 Determinants and Cramer’s Rule What am I Supposed to learn? The Determinant of a 2 × 2 Matrix Solving Systems of Linear Equations in Two Variables Using Determinants The Determinant of a 3 × 3 Matrix Solving Systems of Linear Equations in Three Variables Using Determinants The Determinant of Any n × n Matrix CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 6 Summary, Review, and Test SUMMARY REVIEW EXERCISES 6.1 6.2 6.3 6.4 6.5 CHAPTER 6 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–6) CHAPTER 7 Conic Sections Section 7.1 The Ellipse What am I Supposed to learn? Definition of an Ellipse Standard Form of the Equation of an Ellipse Using the Standard Form of the Equation of an Ellipse Translations of Ellipses Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 7.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 7.2 The Hyperbola What am I Supposed to learn? Definition of a Hyperbola Standard Form of the Equation of a Hyperbola Using the Standard Form of the Equation of a Hyperbola The Asymptotes of a Hyperbola Graphing Hyperbolas Centered at the Origin Translations of Hyperbolas Applications CONCEPT AND VOCABULARY CHECK EXERCISE SET 7.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises CHAPTER 7 Mid-Chapter Check Point Section 7.3 The Parabola What am I Supposed to learn? Definition of a Parabola Standard Form of the Equation of a Parabola Using the Standard Form of the Equation of a Parabola Translations of Parabolas Applications Degenerate Conic Sections Identifying Conic Sections without Completing the Square CONCEPT AND VOCABULARY CHECK EXERCISE SET 7.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 7 Summary, Review, and Test SUMMARY REVIEW EXERCISES 7.1 7.2 7.3 CHAPTER 7 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–7) CHAPTER 8 Sequences, Induction, and Probability Section 8.1 Sequences and Summation Notation What am I Supposed to learn? Sequences Recursion Formulas Factorial Notation Summation Notation CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.1 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 8.2 Arithmetic Sequences What am I Supposed to learn? Arithmetic Sequences The General Term of an Arithmetic Sequence The Sum of the First n Terms of an Arithmetic Sequence CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.2 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 8.3 Geometric Sequences and Series What am I Supposed to learn? Geometric Sequences The General Term of a Geometric Sequence The Sum of the First n Terms of a Geometric Sequence Annuities Geometric Series CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.3 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises CHAPTER 8 Mid-Chapter Check Point Section 8.4 Mathematical Induction What am I Supposed to learn? The Principle of Mathematical Induction SOLUTION Check Point 1  Proving Statements about Positive Integers Using Mathematical Induction SOLUTION Check Point 2 SOLUTION Check Point 3 SOLUTION Check Point 4 CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.4 Practice Exercises Practice Plus Explaining the Concepts Critical Thinking Exercises Group Exercise Retaining the Concepts Preview Exercises Section 8.5 The Binomial Theorem What am I Supposed to learn? Binomial Coefficients The Binomial Theorem Finding a Particular Term in a Binomial Expansion CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.5 Practice Exercises Practice Plus Application Exercises Explaining the Concepts Technology Exercises Critical Thinking Exercises Retaining the Concepts Preview Exercises Section 8.6 Counting Principles, Permutations, and Combinations What am I Supposed to learn? The Fundamental Counting Principle Permutations Section 8.7 Probability What am I Supposed to learn? Empirical Probability Theoretical Probability Computing Theoretical Probability without Listing an Event and the Sample Space SOLUTION Check Point 4 SOLUTION Check Point 5 Probability of an Event Not Occurring Or Probabilities with Mutually Exclusive Events Or Probabilities with Events That Are Not Mutually Exclusive SOLUTION Check Point 8 Solution Check Point 9 And Probabilities with Independent Events CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.7 Practice and Application Exercises Explaining the Concepts Critical Thinking Exercises Retaining the Concepts Group Exercise CHAPTER 8 Summary, Review, and Test SUMMARY REVIEW EXERCISES 8.1 8.2 8.3 8.4 8.5 8.6 8.7 CHAPTER 8 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–8) APPENDIX Where Did That Come From? Selected Proofs Section 4.3 Properties of Logarithms The Product Rule Proof The Change-of-Base Property Proof Section 7.1 The Ellipse The Standard Form of the Equation of an Ellipse with a Horizontal Major Axis Centered at the Origin Proof Section 7.2 The Hyperbola The Asymptotes of a Hyperbola Centered at the Origin Proof ANSWERS TO SELECTED EXERCISES CHAPTER P Section P.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET P.1 Section P.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET P.2 Section P.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET P.3 Section P.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET P.4 Mid-Chapter P Check Point Section P.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET P.5 Section P.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set P.6 Chapter P Review Exercises Chapter P Test CHAPTER 1 Section 1.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.1 Section 1.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.2 Section 1.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.3 Section 1.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.4 Section 1.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.5 Mid-Chapter 1 Check Point Section 1.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.6 Section 1.7 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 1.7 Chapter 1 Review Exercises Chapter 1 Test CHAPTER 2 Section 2.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 2.1 Section 2.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.2 Section 2.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.3 Section 2.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.4 Mid-Chapter 2 Check Point Section 2.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.5 Section 2.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.6 Section 2.7 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.7 Section 2.8 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 2.8 Chapter 2 Review Exercises Chapter 2 Test Cumulative Review Exercises (Chapters 1–2) CHAPTER 3 Section 3.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 3.1 Section 3.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.2 Section 3.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.3 Section 3.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.4 Mid-Chapter 3 Check Point Section 3.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.5 Section 3.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 3.6 Section 3.7 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 3.7 Chapter 3 Review Exercises Chapter 3 Test Cumulative Review Exercises (Chapters 1–3) CHAPTER 4 Section 4.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.1 Section 4.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.2 Section 4.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.3 Mid-Chapter 4 Check Point Section 4.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.4 Section 4.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 4.5 Chapter 4 REVIEW EXERCISES Chapter 4 Test Cumulative Review Exercises (Chapters 1–4) CHAPTER 5 Section 5.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.1 Section 5.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.2 Section 5.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.3 Section 5.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.4 Mid-Chapter 5 Check Point Section 5.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 5.5 Section 5.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 5.6 Chapter 5 Review Exercises Chapter 5 Test Cumulative Review Exercises (Chapters 1–5) Chapter 6 Section 6.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.1 Section 6.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.2 Section 6.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.3 Mid-Chapter 6 Check Point Section 6.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 6.4 Section 6.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 6.5 Chapter 6 Review Exercises Chapter 6 Test Cumulative Review Exercises (Chapters 1–6) Chapter 7 Section 7.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 7.1 Section 7.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 7.2 Mid-Chapter 7 Check Point Section 7.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 7.3 Chapter 7 Review Exercises Chapter 7 Test Cumulative Review Exercises (Chapters 1–7) CHAPTER 8 Section 8.1 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.1 Section 8.2 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.2 Section 8.3 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.3 Mid-Chapter 8 Check Point Section 8.4 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 8.4 Section 8.5 Check Point Exercises CONCEPT AND VOCABULARY CHECK Exercise Set 8.5 Section 8.6 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.6 Section 8.7 Check Point Exercises CONCEPT AND VOCABULARY CHECK EXERCISE SET 8.7 Chapter 8 Review Exercises Chapter 8 Test Cumulative Review Exercises (Chapters 1–8) CHAPTER P CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 7 CHAPTER 8 Definitions, Rules, and Formulas