Introduction 1 What You''ll Find 1 How This Workbook Is Organized 2 Part 1: Questions 2 Part 2: Answers 3 Beyond the Book 3 Where to Go for Additional Help 3 Part 1: The Questions 5 Chapter 1: Reviewing Algebra Basics 7 The Problems You''ll Work On 7 What to Watch Out For 7 Multiplying Binomials and Trinomials 8 Using Pascal''s Triangle to Multiply Binomials 8 Solving Linear Equations 9 Solving Linear Equations for Variables 9 Solving Linear Inequalities 10 Making Radical Expressions Simpler 10 Working with Complex Expressions 11 Chapter 2: Solving Quadratic Equations and Nonlinear Inequalities 13 The Problems You''ll Work On 13 What to Watch Out For 13 Applying the Square Root Rule on Quadratic Equations 14 Solving Quadratic Equations Using Factoring 14 Using the Quadratic Formula to Solve Equations 15 Recognizing and Solving Quadratic-Like Equations 16 Completing the Square to Solve Quadratic Equations 17 Combining Methods When Solving Quadratic Equations 17 Solving Quadratic Inequalities Using Number Lines 18 Chapter 3: Solving Radical and Rational Equations 21 The Problems You''ll Work On 21 What to Watch Out For 21 Solving Rational Equations 22 Taking on Radical Equations Involving One Radical Term 23 Solving Radical Equations with Multiple Radical Terms 25 Chapter 4: Graphs and Equations of Lines 27 The Problems You''ll Work On 27 What to Watch Out For 27 Sketching Lines Using a Point and Slope 28 Writing Equations of Lines Given Point and Slope 29 Writing Equations of Lines Given Two Points 30 Finding Equations of Parallel Lines 30 Writing Equations of Perpendicular Lines 31 Chapter 5: Functions 33 The Problems You''ll Work On 33 What to Watch Out For 33 Determining a Function''s Domain and Range 34 Finding Inverses of Functions 34 Recognizing Even and Odd Functions 35 Performing the Composition Operation on Functions 36 Creating a Difference-Quotient and Simplifying 36 Evaluating Piecewise Functions for Particular Inputs 37 Chapter 6: Quadratic Functions and Relations 39 The Problems You''ll Work On 39 What to Watch Out For 39 Determining the Vertex and Intercepts of a Parabola 40 Writing Equations of Parabolas in a Standard Form 40 Sketching Graphs of Parabolas 41 Using Quadratic Equations in Applications 42 Chapter 7: Polynomial Functions and Equations 45 The Problems You''ll Work On 45 What to Watch Out For 45 Recognizing the Intercepts of Polynomials 46 Factoring by Grouping to Solve for Intercepts 46 Applying the Rational Root Theorem to Find Roots 47 Performing Synthetic Division to Factor Polynomials 48 Evaluating Polynomials for Input Values 48 Investigating End-Behavior of Polynomials 49 Sketching the Graphs of Polynomial Functions 50 Chapter 8: Rational Functions 51 The Problems You''ll Work On 51 What to Watch Out For 51 Investigating the Domain of a Rational Function 52 Determining a Function''s Removable Discontinuity 52 Evaluating a Function When x Is Infinitely Large or Small 53 Determining a Function''s Infinite Limit 54 Writing Equations of Asymptotes 54 Adding Oblique Asymptotes to the Mix 55 Sketching the Graphs of Rational Functions 55 Chapter 9: Exponential and Logarithmic Functions 57 The Problems You''ll Work On 57 What to Watch Out For 57 Evaluating Exponential Functions for Input 58 Evaluating Exponential Functions in Base e 58 Sketching the Graphs of Exponential Functions 59 Finding Values of Logarithmic Expressions for Given Input 59 Evaluating Natural Logarithms in Bas e e 60 Sketching the Graphs of Log Functions 61 Rewriting a Log Function as Its Exponential Inverse 61 Changing Exponential Functions to Logarithmic Inverses 62 Solving Exponential Equations 62 Solving Logarithmic Equations 63 Chapter 10: Conic Sections 65 The Problems You''ll Work On 65 What to Watch Out For 66 Rewriting Equations of Parabolas in Standard Form 66 Determining a Vertex, Focus, Directrix, and Axis of Symmetry 67 Sketching the Graph of a Parabola 67 Rewriting a Circle''s Equation in Standard Form 68 Identifying the Center and Radius of a Circle 68 Sketching the Graph of a Circle 69 Writing an Ellipse''s Equation in Standard Form 69 Identifying the Center, the Foci, and Axis Endpoints 70 Sketching the Graphs of Ellipses 70 Writing the Equation of a Hyperbola in Standard Form 71 Finding the Center, Foci, and Asymptotes of Hyperbolas 71 Sketching the Graphs of Hyperbolas 72 Chapter 11: Systems of Linear Equations 73 The Problems You''ll Work On 73 What to Watch Out For 73 Solving Systems of Two Linear Equations 74 Performing Row Operations on Linear Equations 74 Solving Systems of Equations with Row Echelon Form 75 Using Reduced Row Echelon Form to Solve Systems 76 Solving Systems of Linear Equations 76 Decomposing Fractions Using Systems of Equations 77 Chapter 12: Systems of Nonlinear Equations and Inequalities 79 The Problems You''ll Work On 79 What to Watch Out For 79 Determining Intersections of Parabolas and Lines 80 Finding Where Two Parabolas Meet 80 Solving for Intersections of Conics 81 Finding the Intersections of Exponential Functions 82 Using Graphing to Solve Systems of Inequalities 83 Chapter 13: Working with Complex Numbers 85 The Problems You''ll Work On 85 What to Watch Out For 85 Rewriting Powers of i as i , - i , 1, or -1 86 Operating on and Simplifying Complex Expressions 86 Multiplying and Simplifying Complex Numbers 87 Using Conjugates to Divide Complex Numbers 88 Solving for Complex Solutions in Quadratic Equations 89 Chapter 14: Matrices 91 The Problems You''ll Work On 91 What to Watch Out For 92 Determining the Dimension and Type of Matrix 92 Adding and Subtracting Matrices 92 Performing Scalar Multiplication on Matrices 93 Multiplying Matrices 93 Determining Inverses of Square Matrices 94 Dividing Matrices Using Inverses 94 Using Matrices to Solve Systems of Equations 95 Chapter 15: Sequences and Series 97 The Problems You''ll Work On 97 What to Watch Out For 97 Writing Terms of a Sequence Given a Rule 98 Finding a General Term for an Arithmetic Sequence 98 Writing a General Term for a Geometric Sequence 98 Recognizing Patterns in Sequences 99 Creating Recursively Defined Sequences 99 Writing More Terms of Special Sequences 99 Finding the Sum of the Terms in a Series 100 Summing Arithmetic Series 100 Determining the Sum of a Geometric Series 101 Computing the Sum of a Special Series 102 Using a Special Formula for the Sum of an Infinite Series 102 Chapter 16: Sets 103 The Problems You''ll Work On 103 What to Watch Out For 103 Creating the Elements of a Set from a Description 104 Performing Set Operations 104 Operating on Sets of Special Numbers 105 Using Venn Diagrams to Solve Problems Involving Sets 106 Enlisting Venn Diagrams to Solve Applications 107 Chapter 17: Counting Techniques and Probability 109 The Problems You''ll Work On 109 What to Watch Out For 110 Solving Problems Using the Multiplication Property 110 Counting How Many Using Permutations 111 Incorporating Combinations in Counting Problems 112 Performing a Binomial Expansion 113 Solving Probability Problems Using Counting Techniques 113 Part 2: The Answers 117 Chapter 18: The Answers 119 Index 499.