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 Base 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
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