Introduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 2 Where to Go from Here 3 Chapter 1: Making Advances in Algebra 5 Bringing Out the Best in Algebraic Properties 5 Making short work of the basic properties 6 Organizing your operations 7 Enumerating Exponential Rules 8 Multiplying and dividing exponents 8 Rooting out exponents 9 Powering up exponents 10 Working with negative exponents 10 Assigning Factoring Techniques 10 Making two terms factor 11 Factoring three terms 12 Factoring four or more terms by grouping 13 Chapter 2: Lining Up Linear Equations 15 Getting the First Degree: Linear Equations 15 Solving basic linear equations 16 Eliminating fractions 16 Lining Up Linear Inequalities 17 Solving basic inequalities 18 Introducing interval notation 19 Absolute Value: Keeping Everything in Line 20 Solving absolute value equations 20 Seeing through absolute value inequality 21 Chapter 3: Making Quick Work of Quadratic Equations 23 Using the Square Root Rule When Possible 24 Solving Quadratic Equations by Factoring 24 Factoring quadratic binomials 25 Factoring quadratic trinomials 26 The Quadratic Formula to the Rescue 27 Realizing rational solutions 27 Investigating irrational solutions 27 Promoting Quadratic-like Equations 28 Solving Quadratic Inequalities 29 Keeping it strictly quadratic 30 Signing up for fractions 31 Increasing the number of factors 33 Chapter 4: Rolling Along with Rational and Radical Equations 35 Rounding Up Rational Equations and Eliminating Fractions 35 Making your least common denominator work for you 36 Proposing proportions for solving rational equations 38 Reasoning with Radicals 39 Squaring both sides of the equation 39 Taking on two radicals 40 Dealing with Negative Exponents 42 Factoring out a negative exponent as a greatest common factor 42 Solving quadratic-like trinomials 43 Fiddling with Fractional Exponents 44 Solving equations by factoring fractional exponents 44 Promoting techniques for working with fractional exponents 44 Chapter 5: Forging Function Facts 47 Describing Function Characteristics 47 Denoting function notation 48 Using function notation to evaluate functions 48 Determining Domain and Range 49 Delving into domain 49 Wrangling with range 50 Counting on Even and Odd Functions 51 Determining whether even or odd 52 Using even and odd functions in graphs 53 Taking on Functions One-to-One 53 Defining which functions are one-to-one 54 Testing for one-to-one functions 54 Composing Functions 55 Composing yourself with functions 55 Composing with the difference quotient 56 Getting into Inverse Functions 57 Finding which functions are inverses 58 Finding an inverse of a function 59 Chapter 6: Graphing Linear and Quadratic Functions 61 Identifying Some Graphing Techniques 61 Finding x- and y-intercepts 62 Reflecting on a graph''s symmetry 62 Mastering the Graphs of Lines 64 Determining the slope of a line 64 Describing two line equations 65 Identifying parallel and perpendicular lines 67 Coming to Terms with the Standard Form of a Quadratic 67 Starting with "a" in the standard form 68 Following "a" with "b" and "c" 69 Eyeing a Quadratic''s Intercepts 69 Finding the one and only y-intercept 69 Getting at the x-intercepts 70 Finding the Vertex of a Parabola 71 Computing vertex coordinates 71 Linking up with the axis of symmetry 72 Sketching a Graph from the Available Information 72 Chapter 7: Pondering Polynomials 75 Sizing Up a Polynomial Equation 75 Identifying Intercepts and Turning Points 76 Interpreting relative value and absolute value 76 Dealing with intercepts and turning points 77 Solving for y-intercepts and x-intercepts 78 Determining When a Polynomial is Positive or Negative 79 Incorporating a sign line 79 Recognizing a sign change rule 80 Solving Polynomial Equations 81 Factoring for roots 81 Taking sane steps with the rational root theorem 82 Putting Descartes in charge of signs 84 Finding Roots Synthetically 86 Using synthetic division when searching for roots 86 Synthetically dividing by a binomial 88 Chapter 8: Being Respectful of Rational Functions 91 Examining Rational Functions 91 Deliberating on domain 92 Investigating intercepts 92 Assigning Roles to Asymptotes 93 Validating vertical asymptotes 93 Finding equations for horizontal asymptotes 94 Taking vertical and horizontal asymptotes to graphs 94 Getting the scoop on oblique (slant) asymptotes 96 Discounting Removable Discontinuities 97 Finding removable discontinuities by factoring 97 Evaluating the removals 98 Looking at Limits of Rational Functions 99 Determining limits at function discontinuities 100 Finding infinity 102 Looking at infinity 104 Chapter 9: Examining Exponential and Logarithmic Functions 107 Computing Exponentially 107 Getting to the Base of Exponential Functions 108 Classifying bases 108 Introducing the more frequently used bases: 10 and e 110 Exponential Equation Solutions 110 Creating matching bases 111 Quelling quadratic patterns 111 Looking into Logarithmic Functions 113 Presenting the properties of logarithms 113 Doing more with logs than sawing 115 Solving Equations Containing Logs 117 Seeing all logs created equal 117 Solving log equations by changing to exponentials 118 Chapter 10: Getting Creative with Conics 121 Posing with Parabolas 122 Generalizing the form of a parabola''s equation 123 Making short work of a parabola''s sketch 124 Changing a parabola''s equation to the standard form 125 Circling around a Conic 126 Getting Eclipsed by Ellipses 127 Determining the shape 129 Finding the foci 130 Getting Hyped for Hyperbolas 130 Including the asymptotes 131 Graphing hyperbolas 132 Chapter 11: Solving Systems of Equations 135 Looking at Solutions Using the Standard Linear-Systems Form 136 Solving Linear Systems by Graphing 136 Interpreting an intersection 137 Tackling the same line 137 Putting up with parallel lines 137 Using Elimination (Addition) to Solve Systems of Equations 138 Finding Substitution to Be a Satisfactory Substitute 139 Variable substituting made easy 139 Writing solutions for coexisting lines 140 Taking on Systems of Three Linear Equations 141 Finding the solution of a system of three linear equations 141 Generalizing with a system solution 143 Increasing the Number of Equations 144 Intersecting Parabolas and Lines 146 Determining if and where lines and parabolas cross paths 147 Determining that there''s no solution 149 Crossing Parabolas with Circles 150 Finding multiple intersections 150 Sifting through the possibilities for solutions 151 Chapter 12: Taking the Complexity Out of Complex Numbers 155 Simplifying Powers of i 156 Getting More Complex with Complex Numbers 157 Performing complex operations 157 Performing complex division by multiplying by the conjugate 158 Simplifying reluctant radicals 159 Unraveling Complex Solutions in Quadratic Equations 160 Investigating Polynomials with Complex Roots 160 Classifying conjugate pairs 161 Making use of complex zeros 161 Chapter 13: Ten (or So) Special Formulas 163 Using Multiplication to Add 163 Factoring in Factorial 164 Picking Out Permutations 164 Collecting Combinations 164 Adding n Integers 165 Adding n Squared Integers 165 Adding Odd Numbers 165 Going for the Geometric 166 Calculating Compound Interest 166 Index 167.