Introduction 1 What You''ll Find 1 How This Workbook Is Organized 2 Part 1: The Questions 2 Part 2: The Answers 3 Beyond the Book 3 Where to Go for Additional Help 4 Part 1: The Questions 5 Chapter 1: Getting Started with Algebra Basics 7 The Problems You''ll Work On 7 What to Watch Out For 7 Identifying Which System or Systems a Number Belongs To 8 Recognizing Properties of Number Systems 9 Simplifying Expressions with the Order of Operations 9 Graphing Inequalities 10 Using Graphing Formulas 11 Applying Graphing Formulas 11 Chapter 2: Solving Some Equations and Inequalities 13 The Problems You''ll Work On 13 What to Watch Out For 13 Using Interval and Inequality Notation 14 Solving Linear Inequalities 15 Solving Quadratic Inequalities 15 Solving Absolute Value Inequalities 15 Working with Radicals and Fractional Notation 16 Performing Operations Using Fractional Exponents 16 Factoring Using Fractional Notation 16 Solving Radical Equations 17 Rationalizing Denominators 18 Chapter 3: Function Basics 19 The Problems You''ll Work On 19 What to Watch Out For 19 Using Function Notation to Evaluate Function Values 20 Determining the Domain and Range of a Function 20 Recognizing Even Functions 21 Identifying Odd Functions 21 Ruling Out Even and Odd Functions 21 Recognizing One-to-One Functions from Given Relations 22 Identifying One-to-One Functions from Equations 23 Recognizing a Function''s Inverse 23 Determining a Function''s Inverse 24 Executing Operations on Functions 24 Performing Function Composition 25 Doing More Function Composition 25 Using the Difference Quotient 26 Chapter 4: Graphing and Transforming Functions 27 The Problems You''ll Work On 27 What to Watch Out For 28 Functions and Their Inverses 28 Sketching Quadratic Functions from Their Equations 29 Writing Equations from Graphs of Parabolas 29 Investigating and Graphing Radical Functions 30 Investigating Absolute Value Functions 31 Investigating the Graphs of Polynomial Functions 31 Investigating Rational Functions 32 Transformation of Functions 32 Transforming Selected Points Using Functions 33 Sketching Graphs Using Basic Functions and Transformations 33 Sketching More Graphs Using Basic Functions and Transformations 34 Chapter 5: Polynomials 35 The Problems You''ll Work On 35 What to Watch Out For 36 Using Factoring to Solve Quadratic Equations 36 Solving Quadratic Equations by Using the Quadratic Formula 37 Using Completing the Square to Solve Quadratic Equations 37 Solving Polynomial Equations for Intercepts 37 Using Factoring by Grouping to Solve Polynomial Equations 38 Applying Descartes''s Rule of Signs 38 Listing Possible Roots of a Polynomial Equation 39 Dividing Polynomials 39 Using Synthetic Division to Divide Polynomials 39 Checking for Roots of a Polynomial by Using Synthetic Division 40 Writing Polynomial Expressions from Given Roots 40 Writing Polynomial Expressions When Given Roots and a Point 40 Graphing Polynomials 41 Writing Equations from Graphs of Polynomials 41 Chapter 6: Exponential and Logarithmic Functions 43 The Problems You''ll Work On 43 What to Watch Out For 44 Understanding Function Notation 44 Graphing Exponential Functions 44 Solving Exponential Equations 45 Using the Equivalence b y b y x x log = to Rewrite Expressions 46 Using the Equivalence log b y x b x y to Rewrite Expressions 46 Rewriting Logarithmic Expressions 46 Rewriting Logs of Products and Quotients as Sums and Differences 47 Solving Logarithmic Equations 47 Applying Function Transformations to Log Functions 48 Applying Logarithms to Everyday Life 49 Chapter 7: Trigonometry Basics 51 The Problems You''ll Work On 51 What to Watch Out For 52 Using Right Triangles to Determine Trig Functions 52 Solving Problems by Using Right Triangles and Their Functions 53 Working with Special Right Triangles 54 Changing Radians to Degrees 55 Changing Degrees to Radians 55 Finding Angle Measures (in Degrees) in Standard Position 55 Determining Angle Measures (in Radians) in Standard Position 55 Identifying Reference Angles 56 Determining Trig Functions by Using the Unit Circle 56 Calculating Trig Functions by Using Other Functions and Terminal Side Positions 56 Using the Arc Length Formula 57 Evaluating Inverse Functions 57 Solving Trig Equations for x in Degrees 58 Calculating Trig Equations for x in Radians 58 Chapter 8: Graphing Trig Functions 59 The Problems You''ll Work On 59 What to Watch Out For 60 Recognizing Basic Trig Graphs 60 Graphing Sine and Cosine 62 Applying Function Transformations to Graphs of Trig Functions 62 Writing New Trig Functions Using Transformations 62 Graphing Tangent and Cotangent 63 Interpreting Transformations of Trig Functions 63 Graphing Secant and Cosecant 64 Interpreting Transformations from Function Rules 64 Chapter 9: Getting Started with Trig Identities 65 The Problems You''ll Work On 65 What to Watch Out For 66 Proving Basic Trig Identities 66 Returning to Basic Sine and Cosine to Solve Identities 67 Using Multiplication by a Conjugate to Solve Identities 68 Solving Identities After Raising a Binomial to a Power 68 Solving Identities After Factoring out a Common Function 69 Solving Identities After Combining Fractions 69 Performing Algebraic Processes to Make Identities More Solvable 69 Chapter 10: Continuing with Trig Identities 71 The Problems You''ll Work On 71 What to Watch Out For 71 Using Identities That Add or Subtract Angle Measures 72 Confirming Double-Angle Identities 72 Using Identities That Double the Size of the Angle 72 Confirming the Statements of Multiple-Angle Identities 72 Creating Half-Angle Identities from Double-Angle Identities 73 Creating a Half-Angle Identity for Tangent 73 Using Half-Angle Identities to Simplify Expressions 73 Creating Products of Trig Functions from Sums and Differences 73 Using Product-to-Sum Identities to Evaluate Expressions 74 Using Sum-to-Product Identities to Evaluate Expressions 74 Applying Power-Reducing Identities 74 Using Identities to Determine Values of Functions at Various Angles 75 Working through Identities Using Multiple Methods 75 Chapter 11: Working with Triangles and Trigonometry 77 The Problems You''ll Work On 77 What to Watch Out For 78 Applying the Law of Sines to Find Sides 78 Utilizing the Law of Sines to Find Angles 78 Using the Law of Sines for Practical Applications 79 Investigating the Ambiguous Case of the Law of Sines 79 Determining All Angles and Sides of a Triangle 80 Finding Side Measures by Using the Law of Cosines 80 Using the Law of Cosines to Determine an Angle 80 Applying the Law of Cosines to Real-World Situations 81 Finding Areas of Triangles by Using the Sine 81 Applying the Trig Formula for Area of a Triangle 82 Using the Trig Formula for Area in Various Situations 82 Solving Area Problems Needing Additional Computations 83 Finding Areas of Triangles by Using Heron''s Formula 84 Applying Heron''s Formula 84 Practical Applications Using Heron''s Formula 85 Tackling Practical Applications by Using Triangular Formulas 85 Chapter 12: Complex Numbers and Polar Coordinates 87 The Problems You''ll Work On 87 What to Watch Out For 88 Writing Powers of i in Their Simplest Form 88 Adding and Subtracting Complex Numbers 88 Multiplying Complex Numbers 89 Using Multiplication to Divide Complex Numbers 90 Solving Quadratic Equations with Complex Solutions 90 Graphing Complex Numbers 91 Identifying Points with Polar Coordinates 92 Identifying Points Whose Angles Have Negative Measures 93 Converting Polar to Rectangular Coordinates 93 Converting Rectangular to Polar Coordinates 94 Recognizing Polar Curves 94 Chapter 13: Conic Sections 95 The Problems You''ll Work On 95 What to Watch Out For 95 Identifying Conics from Their Equations 96 Rewriting Conic Equations in Standard Form 96 Writing Equations for Circles 97 Determining Foci and Axes of Symmetry of Parabolas 97 Finding the Vertices and Directrixes of Parabolas 98 Writing Equations of Parabolas 98 Determining Centers and Foci of Ellipses 98 Writing Equations of Ellipses 99 Determining Asymptotes of Hyperbolas 99 Writing Equations of Hyperbolas 99 Changing Equation Format from Trig Functions to Algebraic 100 Changing Equation Format from Algebraic to Trig 100 Chapter 14: Systems of Equations and Inequalities 101 The Problems You''ll Work On 101 What to Watch Out For 102 Using Substitution to Solve Systems of Linear Equations with Two Variables 102 Using Elimination to Solve Systems of Linear Equations with Two Variabl.