Precalculus: Functions and Graphs

by Demana, Franklin; Waits, Bert K.; Foley, Gregory D.; Kennedy, Daniel

• ISBN13: 9780201611366
• ISBN10: 0201611368
• Edition: 4th
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Addison Wesley

Summary

This text, intended for a graphing calculator required precalculus course, shows students when and how to use concepts, and promotes real understanding not just rote memorization. In addition, the graphing calculator is used as a tool to help explain ideas rather than merely to find answers. The book reflects AMATYC, MAA, and NCTM guidelines, and makes use of real world data in presenting a balanced algebraic and graphical approach to understanding precalculus concepts. The result is a thorough preparation for the calculus course.

Table of Contents

Prerequisites
Real Numbers	1	(10)
Cartesian Coordinate System	11	(8)
Linear Equations and Inequalities	19	(7)
Lines in the Plane	26	(12)
Solving Equations Graphically, Numerically and Algebraically	38	(10)
Solving Inequalities Algebraically and Graphically	48	(13)
Key Ideas	55	(2)
Review Exercises	57	(4)
Functions and Graphs
Modeling and Equation Solving	61	(17)
Functions and Their Properties	78	(21)
Ten Basic Functions	99	(8)
Building Functions from Functions	107	(18)
Graphical Transformations	125	(10)
Modeling with Functions	135	(20)
Math at Work	147	(1)
Key Ideas	148	(2)
Review Exercises	150	(3)
Chapter Project	153	(2)
Polynomial, Power and Rational Functions
Linear and Quadratic Functions with Modeling	155	(19)
Power Functions with Modeling	174	(12)
Polynomial Functions of Higher Degree with Modeling	186	(13)
Real Zeros of Polynomial Functions	199	(13)
Complex Numbers	212	(8)
Complex Zeros and the Fundamental Theorem of Algebra	220	(7)
Rational Functions and Equations	227	(12)
Solving Inequalities in One Variable	239	(20)
Math at Work	249	(1)
Key Ideas	249	(4)
Review Exercises	253	(4)
Chapter Project	257	(2)
Exponential, Logistic, and Logarithmic Functions
Exponential and Logistic Functions	259	(13)
Exponential and Logistic Modeling	272	(10)
Logarithmic Functions and Their Graphs	282	(11)
Properties of Logarithmic Functions	293	(9)
Equation Solving and Modeling	302	(13)
Mathematics of Finance	315	(22)
Key Ideas	327	(4)
Review Exercises	331	(4)
Chapter Project	335	(2)
Trigonometric Functions
Angles and Their Measures	337	(8)
Trigonometric functions of Acute Angles	345	(10)
Trigonometry Extended: The Circular Functions	355	(13)
Graphs of Sine and Cosine: Sinusoids	368	(11)
Graphs of Tangent, Cotangent, Secant, and Cosecant	379	(8)
Graphs of Composite Trigonometric Functions	387	(7)
Inverse Trigonometric Functions	394	(10)
Solving Problems with Trigonometry	404	(19)
Key Ideas	416	(2)
Review Exercises	418	(3)
Chapter Project	421	(2)
Analytic Trigonometry
Fundamental Identities	423	(9)
Proving Trigonometric Identities	432	(7)
Sum and Difference Identities	439	(7)
Multiple-Angle Identities	446	(7)
Law of Sines	453	(8)
Law of Cosines	461	(18)
Math at Work	471	(1)
Key Ideas	471	(2)
Review Exercises	473	(4)
Chapter Project	477	(2)
Vectors, Parametric Equations, and Polar Equations
Vectors in the Plane	479	(11)
Dot Products of Vectors	490	(7)
Parametric Equations and Motion	497	(13)
Polar Coordinates	510	(7)
Graphs of Polar Equations	517	(8)
De Moivre's Theorem and nth Roots	525	(18)
Key Ideas	534	(3)
Review Exercises	537	(3)
Chapter Project	540	(3)
Systems and Matrices
Solving Systems of Two Equations	543	(9)
Matrix Algebra	552	(15)
Multivariate Linear Systems and Row Operations	567	(13)
Partial Fractions	580	(7)
Systems of Inequalities in Two Variables	587	(16)
Math at Work	595	(1)
Key Ideas	595	(2)
Review Exercises	597	(4)
Chapter Project	601	(2)
Analytic Geometry in Two and Three Dimensions
Conic Sections and Parabolas	603	(11)
Ellipses	614	(10)
Hyperbolas	624	(11)
Translations and Rotations of Axes	635	(7)
Polar Equations of Conics	642	(9)
Three Dimensional Cartesian Coordinate System	651	(18)
Key Ideas	661	(3)
Review Exercises	664	(2)
Chapter Project	666	(3)
Discrete Mathematics
Basic Combinatorics	669	(9)
The Binomial Theorem	678	(5)
Probability	683	(13)
Sequences and Series	696	(15)
Mathematical Induction	711	(6)
Statistics and Data (Graphical)	717	(13)
Statistics and Data (Algebraic)	730	(23)
Math at Work	744	(1)
Key Ideas	744	(3)
Review Exercises	747	(4)
Chapter Project	751	(2)
An Introduction to Calculus: Limits, Derivatives, and Integrals
Limits and Motion: The Tangent Problem	753	(10)
Limits and Motion: The Area Problem	763	(8)
More on Limits	771	(13)
Numerical Derivatives and Integrals	784	(13)
Key Ideas	791	(3)
Review Exercises	794	(2)
Chapter Project	796	(1)
Appendix A: Algebra Review	797	(18)
A.1 Radicals and Rational Exponents	797	(5)
A.2 Polynomials and Factoring	802	(6)
A.3 Fractional Expressions	808	(7)
Glossary	815	(16)
Selected Answers	831	(114)
Applications Index	945	(4)
Index	949