Precalculus : Functions and Graphs: A Graphing Approach

by LARSON

• ISBN13: 9780669352061
• ISBN10: 0669352063
• Edition: 1st
• Format: Paperback
• Copyright: 1993-01-02
• Publisher: Brooks Cole

Table of Contents

Introduction to Calculators	xxviii
Prerequisites Review of Basic Algebra	1	(56)
The Real Number System	1	(7)
Properties of Real Numbers and the Basic Rules of Algebra	8	(10)
Radicals and Rational Exponents	18	(8)
Polynomials and Special Products	26	(4)
Factoring	30	(6)
Fractional Expressions	36	(7)
The Cartesian Plane	43	(6)
Exploring Data: Representing Data Graphically	49	(8)
Functions and Graphs	57	(78)
Graphs and Graphing Utilities	57	(11)
Lines in the Plane	68	(13)
Functions	81	(13)
Graphs of Functions	94	(11)
Shifting, Reflecting, and stretching Graphs	105	(9)
Combinations of Functions	114	(9)
Inverse Functions	123	(12)
Review Exercises	132	(3)
Intercepts, Zeros, and Solutions	135	(74)
Linear Equations and Modeling	135	(12)
Solving Equations Graphically	147	(10)
Complex Numbers	157	(9)
Solving Equations Algebraically	166	(15)
Solving Inequalities Algebraically and Graphically	181	(14)
Exploring Data: Linear Models and Scatter Polts	195	(14)
Review Exercises	204	(3)
Cumulative Test for Prerequisites, Chapter 1 and 2	207	(2)
Polynomial and Rational Functions	209	(73)
Quadratic Functions	209	(11)
Polynomial Functions of Higher Degree	220	(11)
Real Zeros of Polynomial Functions	231	(17)
Complex Zeros and the Fundamental Theorem of Algebra	248	(7)
Rational Functions and Asymptotes	255	(10)
Graphs of Rational Functions	265	(17)
Review Exercises	275	(7)
Exponential and Logarithmic functions	282	(59)
Exponential Functions and Their Graphs	279	(12)
Logarithmic Functions and Their Graphs	291	(10)
Properties of Logarithms	301	(8)
Solving Exponential and Logarithmic Equations	309	(9)
Applications of Exponential and Logarithmic Functions	318	(12)
Exploring Data: Nonlinear Models	330	(11)
Review Exercises	337	(4)
Trigonometric Functions	341	(100)
Radian and Degree Measure	341	(13)
The Trigonometric Functions and the Unit Circle	354	(9)
Trigonometric Functions and Right Triangles	363	(12)
Trigonometric Functions of Any Angle	375	(11)
Graphs of Sine and Cosine Functions	386	(12)
Other Trigonometric Graphs	398	(13)
Inverse Trigonometric Functions	411	(11)
Applications of Trigonometry	422	(19)
Review Exercises	435	(3)
Cumulative Test For Chapters 3-5	438	(3)
Additional Topics in Trigonometry	441	(82)
Applications of Fundamental Indentities	441	(9)
Verifying Trigonometric Identities	450	(7)
Solving Trigonometric Equations	457	(12)
Sum and Difference Formulas	469	(8)
Multiple-Angle and Product-to-Sum Formulas	477	(11)
Law of Sines	488	(11)
Law of Cosines	499	(9)
Demoivre's theorem and Nth Roots	508	(15)
Review Exercises	519	(4)
Linear Models and Systems of Equations	523	(130)
Solving Systems of Equations Algebraically and Graphically	523	(11)
Systems of Linear Equations in Two Variables	534	(12)
Systems of Linear Equations in More Than Two Variables	546	(12)
Partial Fractions	558	(8)
Systems of Inequalities	566	(10)
Linear Programming	576	(17)
Review Exercises	589	(4)
Matrices and Determinants
Matrices and Systems of Linear Equations	593	(12)
Operations with Matrices	605	(14)
Inverse Matrices and Systems of Linear Equations	619	(7)
The Determinant of a Square Matrix	626	(10)
Applications of Matrices and Determinants	636	(17)
Review Exercises	649	(2)
Cumulative Test for Chapters 6-8	651	(2)
Sequences, Probability, and Statistics	653	(98)
Sequences and Summation Notation	653	(11)
Arithmetic Sequences	664	(12)
Geometric Sequences	676	(9)
Mathematical Induction	685	(11)
The Binomial Theorem	696	(9)
Counting Principles, Permutations, Combinations	705	(13)
Probability	718	(13)
Exploring Data: Measures of Central Tendency	731	(8)
Exploring Data: Measures of Dispersion	739	(12)
Review Exercises	748	(3)
Conics, Parametric Equations, and Polar Coordinates	751	(74)
INtroduction to Conics: Parabolas	751	(9)
Ellipses	760	(9)
Hyperbolas	769	(9)
Rotation and Systems of Quadratic Equations	778	(9)
Plane Curves and Parametric Equations	787	(9)
Polar Coordinates	796	(8)
Graphs of Polar Equations	804
Polar Coordinates	796	(8)
Graphs of Polar Equations	804	(9)
Polar Equations of Conics	813	(12)
Review Exercises	822	(3)
Vectors in the Plane	825
Fectors in the Plane	825
The Dot Product of Two Vectors	839
Review Exercises	834
Cumulative Test for Chapters 9-11	850
APPENDIXES
Appendix A: Graphing Utilities	A1
Appendix B: Programs	A11
Appendix C: Fractal Programs	A27
ANSWES
Warm-Ups, ODD-Numbered Exercises, Cumulative Tests	A29
INDEXES
Index of Applications	A111
Index	A115