Precalculus: Functions & Graphs

Description

Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course. The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and ""user-friendly"". Progress checks, warnin.;Front Cover; Precalculus: Functions & Graphs; Copyright Page; Table of Contents; Dedication; PREFACE; ACKNOWLEDGMENTS; TO THE STUDENT; CHAPTER 1. THE FOUNDATIONS OF ALGEBRA; 1.1 THE REAL NUMBER SYSTEM; 1.2 POLYNOMIALS AND FACTORING; 1.3 EXPONENTS, RADICALS, ANDCOMPLEX NUMBERS; 1.4 LINEAR EQUATIONS AND LINEAR INEQUALITIES IN ONE UNKNOWN; 1.5 ABSOLUTE VALUE IN EQUATIONS AND INEQUALITIES; 1.6 SECOND-DEGREE INEQUALITIES; CHAPTER 2. FUNCTIONS AND GRAPHS; 2.1 THE RECTANGULAR COORDINATE SYSTEM; 2.2 FUNCTIONS AND FUNCTION NOTATION; 2.3 GRAPHS OF FUNCTIONS; 2.4 AIDS IN GRAPHING; 2.5 LINEAR FUNCTIONS. Front Cover Precalculus: Functions & Graphs Copyright Page Table of Contents Dedication PREFACE ACKNOWLEDGMENTS TO THE STUDENT CHAPTER 1. THE FOUNDATIONS OF ALGEBRA 1.1 THE REAL NUMBER SYSTEM 1.2 POLYNOMIALS AND FACTORING 1.3 EXPONENTS, RADICALS, ANDCOMPLEX NUMBERS 1.4 LINEAR EQUATIONS AND LINEAR INEQUALITIES IN ONE UNKNOWN 1.5 ABSOLUTE VALUE IN EQUATIONS AND INEQUALITIES 1.6 SECOND-DEGREE INEQUALITIES CHAPTER 2. FUNCTIONS AND GRAPHS 2.1 THE RECTANGULAR COORDINATE SYSTEM 2.2 FUNCTIONS AND FUNCTION NOTATION 2.3 GRAPHS OF FUNCTIONS 2.4 AIDS IN GRAPHING 2.5 LINEAR FUNCTIONS. 2.6 QUADRATIC EQUATIONS2.7 QUADRATIC FUNCTIONS 2.8 COMBINING FUNCTIONS INVERSE FUNCTIONS CHAPTER 3. ROOTS OF POLYNOMIALS 3.1 SYNTHETIC DIVISION THE REMAINDER AND FACTOR THEOREMS 3.2 GRAPHS OF POLYNOMIAL FUNCTIONS 3.3 THE RATIONAL ROOTTHEOREM AND THE DEPRESSED EQUATION 3.4 RATIONAL FUNCTIONSAND THEIR GRAPHS 3.5 PARTIAL FRACTIONS CHAPTER 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 4.1 EXPONENTIAL FUNCTIONS 4.2 LOGARITHMIC FUNCTIONS 4.3 FUNDAMENTAL PROPERTIES OF LOGARITHMS 4.4 COMPUTING WITH LOGARITHMS (Optional 4.5 EXPONENTIAL AND LOGARITHMIC EQUATIONS. CHAPTER 5. TRIGONOMETRY: THE CIRCULAR FUNCTIONS5.0 REVIEW OF GEOMETRY 5.1 THE WRAPPING FUNCTION 5.2 THE SINE, COSINE, AND TANGENT FUNCTIONS 5.3 GRAPHS OFSINE, COSINE, AND TANGENT 5.4 VALUES OFSINE, COSINE, AND TANGENT 5.5 GRAPHS:AMPLITUDE, PERIOD, AND PHASE SHIFT 5.6 SECANT, COSECANT, AND COTANGENT 5.7 THE INVERSE TRIGONOMETRIC FUNCTIONS CHAPTER 6. ANGLES AND TRIANGLES 6.1 ANGLES AND THEIRMEASUREMENT 6.2 TRIGONOMETRIC FUNCTIONS OF ANGLES 6.3 RIGHT TRIANGLE TRIGONOMETRY 6.4 LAW OF COSINES 6.5 LAW OF SINES CHAPTER 7. ANALYTIC TRIGONOMETRY 7.1 TRIGONOMETRIC IDENTITIES. 7.2 THE ADDITION FORMULAS7.3 DOUBLE- ANDHALF-ANGLE FORMULAS 7.4 THE PRODUCT-SUM FORMULAS 7.5 TRIGONOMETRIC EQUATIONS CHAPTER 8. COMPLEX NUMBERS AND THE FUNDAMENTAL THEOREM OF ALGEBRA 8.1 COMPLEX NUMBERS AND THEIRPROPERTIES 8.2 TRIGONOMETRY AND COMPLEX NUMBERS 8.3 THE FUNDAMENTAL THEOREM OF ALGEBRA 8.4 DESCARTES'S RULE OF SIGNS CHAPTER 9. ANALYTIC GEOMETRY: THE CONIC SECTIONS 9.1 ANALYTIC GEOMETRY 9.2 THE CIRCLE 9.3 THE PARABOLA 9.4 THE ELLIPSE 9.5 THE HYPERBOLA 9.6 TRANSLATION OF AXES 9.7 ROTATION OF AXES 9.8 POLAR COORDINATES 9.9 PARAMETRIC EQUATIONS. CHAPTER 10. SYSTEMS OF EQUATIONS AND INEQUALITIES10.1 SYSTEMS OF EQUATIONS 10.2 SYSTEMS OF LINEAR INEQUALITIES 10.3 LINEAR PROGRAMMING (Optional) 10.4 SYSTEMS OF LINEAR EQUATIONS IN THREE UNKNOWNS 10.5 MATRICES AND LINEAR SYSTEMS 10.6 MATRIX OPERATIONS AND APPLICATIONS (Optional) 10.7 INVERSES OF MATRICES (Optional) 10.8 DETERMINANTS AND CRAMER'S RULE CHAPTER 11. SEQUENCES AND SERIES 11.1 SEQUENCES AND SIGMA NOTATION 11.2 ARITHMETIC SEQUENCES 11.3 GEOMETRIC SEQUENCES 11.4 MATHEMATICAL INDUCTION 11.5 THE BINOMIAL THEOREM APPENDIX A: APPLICATIONS.