Contemporary Precalculus: A Graphing Approach

by Hungerford, Thomas W.

• ISBN13: 9780030259890
• ISBN10: 0030259894
• Edition: 3rd
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Brooks Cole

Summary

Hungerford approaches the subject of precalculus by integrating graphing technology into the course without losing sight of the fact that the underlying mathematics is the crucial issue. Mathematics is presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving.

Table of Contents

Preface	ix
To the Instructor	xx
To the Student	xxiv
Basics	1	(58)
The Real Number System	2	(16)
Excursion: Decimal Representation of Real Numbers	15	(3)
Solving Equations Algebraically	18	(10)
Excursion: Absolute Value Equations	26	(2)
The Coordinate Plane	28	(10)
Lines	38	(21)
Chapter Review	51	(8)
Graphs and Technology	59	(58)
Graphs and Graphing Calculators	60	(13)
Solving Equations Graphically and Numerically	73	(7)
Applications of Equations	80	(11)
Optimization Applications	91	(5)
Linear Models	96	(21)
Chapter Review	109	(8)
Functions and Graphs	117	(88)
Functions	118	(9)
Functional Notation	127	(9)
Graphs of Functions	136	(14)
Graphs and Transformations	150	(15)
Excursion: Symmetry	159	(6)
Operations on Functions	165	(9)
Rates of Change	174	(12)
Inverse Functions	186	(19)
Chapter Review	195	(10)
Polynomial and Rational Functions	205	(100)
Quadratic Functions	206	(7)
Polynomial Functions	213	(11)
Excursion: Synthetic Division	221	(3)
Real Roots of Polynomials	224	(8)
Graphs of Polynomial Functions	232	(17)
Excursion: Polynomial Models	244	(5)
Rational Functions	249	(18)
Excursion: Other Rational Functions	263	(4)
Polynomial and Rational Inequalities	267	(14)
Excursion: Absolute Value Inequalities	278	(3)
Complex Numbers	281	(7)
Theory of Equations	288	(17)
Chapter Review	295	(10)
Exponential and Logarithmic Functions	305	(84)
Radicals and Rational Exponents	306	(14)
Excursion: Radical Equations	313	(7)
Exponential Functions	320	(20)
Excursion: Compound Interest and the Number e	334	(6)
Common and Natural Logarithmic Functions	340	(20)
Excursion: Logarithmic Functions to Other Bases	352	(8)
Algebraic Solutions of Exponential and Logarithmic Equations	360	(9)
Exponential, Logarithmic, and Other Models	369	(20)
Chapter Review	381	(8)
Trigonometric Functions	389	(76)
Angles and Their Measurement	390	(11)
The Sine, Cosine, and Tangent Functions	401	(8)
Algebra and Identities	409	(9)
Basic Graphs	418	(10)
Periodic Graphs and Simple Harmonic Motion	428	(19)
Excursion: Other Trigonometric Graphs	441	(6)
Other Trigonometric Functions	447	(18)
Chapter Review	456	(9)
Triangle Trigonometry	465	(42)
Right Triangle Trigonometry	466	(15)
The Law of Cosines	481	(7)
The Law of Sines	488	(19)
Chapter Review	501	(6)
Trigonometric Identities and Equations	507	(56)
Basic Identities and Proofs	508	(9)
Addition and Subtraction Identities	517	(13)
Excursion: Lines and Angles	526	(4)
Other Identities	530	(8)
Trigonometric Equations	538	(11)
Inverse Trigonometric Functions	549	(14)
Chapter Review	557	(6)
Applications of Trigonometry	563	(46)
The Complex Plane and Polar Form for Complex Numbers	564	(6)
DeMoivre's Theorem and nth Roots of Complex Numbers	570	(8)
Vectors in the Plane	578	(15)
The Dot Product	593	(16)
Chapter Review	603	(6)
Analytic Geometry	609	(72)
Plane Curves and Parametric Equations	610	(14)
Conic Sections	624	(14)
Translations and Rotations of Conics	638	(17)
Excursion: Rotation of Axes	649	(6)
Polar Coordinates	655	(9)
Polar Equations of Conics	664	(17)
Chapter Review	675	(6)
Systems of Equations	681	(50)
Systems of Linear Equations in Two Variables	682	(11)
Large Systems of Linear Equations	693	(15)
Matrix Methods for Square Systems	708	(11)
Systems of Nonlinear Equations	719	(12)
Chapter Review	726	(5)
Discrete Algebra	731	(48)
Sequences and Sums	732	(10)
Arithmetic Sequences	742	(5)
Geometric Sequences	747	(10)
Excursion: Infinite Series	752	(5)
The Binomial Theorem	757	(7)
Mathematical Induction	764	(15)
Chapter Review	774	(5)
Algebra Review Appendix	779	(18)
Geometry Review Appendix	797	(6)
Program Appendix	803	(4)
Answers to Odd-Numbered Exercises	807
Index of Applications	1	(4)
Index	5