Precalculus Functions and Graphs

by Swokowski, Earl W.; Cole, Jeffery A.

• ISBN13: 9780534352639
• ISBN10: 0534352634
• Format: Hardcover
• Copyright: 1997-12-29
• Publisher: Brooks Cole

Summary

Provides detailed solutions for odd-numbered exercises.

Table of Contents

PREFACE	xiv
CHAPTER 1 TOPICS FROM ALGEBRA	1	(112)
1.1 Real Numbers	2	(13)
1.2 Exponents and Radicals	15	(12)
1.3 Algebraic Expressions	27	(14)
1.4 Equations	41	(16)
1.5 Complex Numbers	57	(6)
1.6 Inequalities	63	(12)
1.7 Rectangular Coordinate Systems	75	(18)
1.8 Lines	93	(16)
CHAPTER 1 REVIEW EXERCISES	109	(3)
CHAPTER 1 DISCUSSION EXERCISES	112	(1)
CHAPTER 2 FUNCTIONS	113	(70)
2.1 Definition of Function	114	(17)
2.2 Graphs of Functions	131	(12)
2.3 Quadratic Functions	143	(14)
2.4 Operations on Functions	157	(10)
2.5 Inverse Functions	167	(10)
CHAPTER 2 REVIEW EXERCISES	177	(4)
CHAPTER 2 DISCUSSION EXERCISES	181	(2)
CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS	183	(56)
3.1 Polynomial Functions of Degree Greater Than 2	184	(8)
3.2 Properties of Division	192	(8)
3.3 Zeros of Polynomials	200	(13)
3.4 Complex and Rational Zeros of Polynomials	213	(8)
3.5 Rational Functions	221	(15)
CHAPTER 3 REVIEW EXERCISES	236	(2)
CHAPTER 3 DISCUSSION EXERCISES	238	(1)
CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS	239	(60)
4.1 Exponential Functions	240	(11)
4.2 The Natural Exponential Function	251	(10)
4.3 Logarithmic Functions	261	(15)
4.4 Properties of Logarithms	276	(8)
4.5 Exponential and Logarithmic Equations	284	(10)
CHAPTER 4 REVIEW EXERCISES	294	(2)
CHAPTER 4 DISCUSSION EXERCISES	296	(3)
CHAPTER 5 THE TRIGONOMETRIC FUNCTIONS	299	(96)
5.1 Angles	300	(9)
5.2 Trigonometric Functions of Angles	309	(16)
5.3 Trigonometric Functions of Real Numbers	325	(19)
5.4 Values of the Trigonometric Functions	344	(7)
5.5 Trigonometric Graphs	351	(15)
5.6 Additional Trigonometric Graphs	366	(9)
5.7 Applied Problems	375	(13)
CHAPTER 5 REVIEW EXERCISES	388	(6)
CHAPTER 5 DISCUSSION EXERCISES	394	(1)
CHAPTER 6 ANALYTIC TRIGONOMETRY	395	(64)
6.1 Verifying Trigonometric Identities	396	(5)
6.2 Trigonometric Equations	401	(12)
6.3 The Addition and Subtraction Formulas	413	(11)
6.4 Multiple-Angle Formulas	424	(10)
6.5 Product-to-Sum and Sum-to-Product Formulas	434	(5)
6.6 The Inverse Trigonometric Functions	439	(15)
CHAPTER 6 REVIEW EXERCISES	454	(3)
CHAPTER 6 DISCUSSION EXERCISES	457	(2)
CHAPTER 7 APPLICATIONS OF TRIGONOMETRY	459	(60)
7.1 The Law of Sines	460	(10)
7.2 The Law of Cosines	470	(10)
7.3 Trigonometric Form for Complex Numbers	480	(5)
7.4 De Moivre's Theorem and nth Roots of Complex Numbers	485	(5)
7.5 Vectors	490	(14)
7.6 The Dot Product	504	(10)
CHAPTER 7 REVIEW EXERCISES	514	(3)
CHAPTER 7 DISCUSSION EXERCISES	517	(2)
CHAPTER 8 SYSTEMS OF EQUATIONS AND INEQUALITIES	519	(90)
8.1 Systems of Equations	520	(9)
8.2 Systems of Linear Equations in Two Variables	529	(8)
8.3 Systems of Linear Equations in More Than Two Variables	537	(15)
8.4 Partial Fractions	552	(6)
8.5 Systems of Inequalities	558	(7)
8.6 Linear Programming	565	(9)
8.7 The Algebra of Matrices	574	(9)
8.8 The Inverse of a Matrix	583	(6)
8.9 Determinants	589	(7)
8.10 Properties of Determinants	596	(8)
CHAPTER 8 REVIEW EXERCISES	604	(3)
CHAPTER 8 DISCUSSION EXERCISES	607	(2)
CHAPTER 9 SEQUENCES, SERIES, AND PROBABILITY	609	(72)
9.1 Infinite Sequences and Summation Notation	610	(9)
9.2 Arithmetic Sequences	619	(7)
9.3 Geometric Sequences	626	(9)
9.4 Mathematical Induction	635	(6)
9.5 The Binomial Theorem	641	(9)
9.6 Permutations	650	(7)
9.7 Distinguishable Permutations and Combinations	657	(7)
9.8 Probability	664	(12)
CHAPTER 9 REVIEW EXERCISES	676	(3)
CHAPTER 9 DISCUSSION EXERCISES	679	(2)
CHAPTER 10 TOPICS FROM ANALYTIC GEOMETRY	681	(69)
10.1 Parabolas	682	(10)
10.2 Ellipses	692	(13)
10.3 Hyperbolas	705	(13)
10.4 Plane Curves and Parametric Equations	718	(10)
10.5 Polar Coordinates	728	(12)
10.6 Polar Equations of Conics	740	(7)
CHAPTER 10 REVIEW EXERCISES	747	(2)
CHAPTER 10 DISCUSSION EXERCISES	749	(1)
APPENDIXES	750
I Using a TI-82/83 Graphing Calculator	750	(38)
II Common Graphs and Their Equations	788	(2)
III A Summary of Graph Transformations	790	(2)
IV Graphs of Trigonometric Functions and Their Inverses	792
ANSWERS TO SELECTED EXERCISES	A1	(84)
INDEX OF APPLICATIONS	A85	(4)
INDEX	A89