Precalculus (CliffsQuickReview Series)
CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side.\ Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other...
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CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side. Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as Arithmetic and algebraic skills Functions and their graphs Polynomials, including binomial expansion Right and oblique angle trigonometry Equations and graphs of conic sections Matrices and their application to systems of equations CliffsQuickReview Precalculus acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. You can either read the book from cover to cover or just look for the information you want and put it back on the shelf for later. What's more, you can Use the free Pocket Guide full of essential information Get a glimpse of what you’ll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center Use the glossary to find key terms fast. With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.
Introduction1Why You Need This Book1How to Use This Book2Visit Our Web Site2Chapter 1Precalculus Prerequisites3Classifying Numbers3Interval Notation5Bounded intervals5Unbounded intervals6Algebraic Properties7The associative property7The commutative property8The distributive property8Identity elements9Inverse properties9Exponential Expressions9Radical Expressions12Properties of radicals12Simplifying radicals12Operations with radicals13Rationalizing expressions14Polynomial Expressions14Classifying polynomials15Adding and subtracting polynomials15Multiplying polynomials16Rational Expressions17Adding and subtracting rational expressions17Multiplying rational expressions18Simplifying complex fractions18Equations and Inequalities19Solving equations19Solving linear inequalities20Solving absolute value inequalities21Special inequality cases22Finding Linear Equations23Chapter 2Functions26Relations vs. Functions26Understanding relations26Defining functions27Writing functions28Function Graphs30The vertical line test31Finding symmetry31Calculating intercepts33Determining domain and range33Eight Key Function Graphs34Basic Function Transformations36Vertical and horizontal shifts37Reflections38Stretching and squishing39Multiple transformations40Combining and Composing Functions41Arithmetic combinations41The composition of functions42Inverse Functions43What is an inverse function?43Graphs of inverse functions44Finding inverse functions44Chapter 3Polynomial and Rational Functions47Factoring Polynomials47Greatest common factors48Factoring by grouping48Factoring quadratic trinomials49Special factor patterns50Solving Quadratic Equations50Factoring51The quadratic formula51Completing the square52Polynomial Division53Long division53Synthetic division55Important Root-Finding Theorems56The remainder theorem56The factor theorem57Calculating Roots58The Fundamental Theorem of Algebra58Descartes' Rule of Signs58The Rational Root Test60Determining roots60Advanced Graphing Techniques62The Leading Coefficient Test62Finding rational asymptotes64Chapter 4Exponential and Logarithmic Functions67Exponential Functions67Natural exponential function68Graphs of exponential functions68Logarithmic Functions70Natural and common logs71Inverse relationship71Graphs of logarithmic functions71Change of base formula73Properties of Logarithms73Solving Exponential and Logarithmic Equations76Exponential equations76Logarithmic equations77Exponential Word Problems79Compound interest79Growth and decay80Chapter 5Trigonometry83Measuring Angles83Characteristics of angles83Degrees and radians84Angle pairs86Coterminal angles87The Unit Circle88Right Triangle Trigonometry91Oblique Triangle Trigonometry94Reference angles95Calculating trigonometric ratios96Graphs of Sine and Cosine98Periodic graphs98Transforming sine and cosine99Other Trigonometric Function Graphs101Inverse Trigonometric Functions103Chapter 6Analytic Trigonometry106Trigonometric Identities106Four types of identities107Simplifying expressions with identities108Proving Trigonometric Identities110Solving Trigonometric Equations111Simple equations113Quadratic equations113Equations requiring identities114Equations requiring squaring115Functions of multiple angles115Sum and Difference Identities116Additional Identities117Double-angle formulas117Half-angle formulas118Sum-product formulas119Product-sum formulas120Oblique Triangle Laws120Law of Sines121Law of Cosines123Calculating Triangle Area124Given Side-Angle-Side125Given side-side-side125Chapter 7Vectors and the Trigonometry of Complex Numbers128Vectors in the Coordinate Plane128Standard form of a vector129Unit vectors130Basic vector operations131Dot Products134Properties of the dot product134Measuring angles between vectors135Orthogonal vectors136Complex Numbers and Trigonometry137Basic operations with complex numbers138Trigonometric form of a complex number140Multiplying and dividing complex numbers141Roots and Powers of Complex Numbers142DeMoivre's Theorem142Calculating nth roots of complex numbers143Chapter 8Analytic Geometry145Conic Sections145Circles146Parabolas148Ellipses153Standard form153Eccentricity156Hyperbolas158Standard form159Graphing hyperbolas160Equations of asymptote lines162Identifying Conic Sections163Parametric Equations163Graphing parametric equations163Rewriting parametric equations164Polar Coordinates165Converting between polar and rectangular coordinates167Converting between polar and rectangular equations168Chapter 9Matrices and Systems of Equations171Systems of Equations171Two-Variable Linear Systems172Substitution method173Elimination method174Nonlinear Systems of Equations175Characteristics of Matrices176Basic Matrix Operations177Adding matrices177Scalar multiplication178Subtracting matrices178Multiplying matrices179Solving Systems of Equations with Matrices180Gaussian and Gauss-Jordan elimination181Matrix row operations182Systems with infinitely many solutions184Inverse Matrices185Calculating inverse matrices186Solving matrix equations187Determinants189Determinants of 2 x 2 matrices189Minors and cofactors189Determinants of square matrices190Cramer's Rule192Graphs of Two-Variable Inequalities194Single inequalities194Systems of inequalities196Linear Programming198Chapter 10Additional Topics201Binomial Expansion201Pascal's Triangle202Factorials204The Binomial Theorem204Ordered Number Lists205Sequences206Series206CQR Resource Center208Glossary for CQR Precalculus210Index217
