Precalculus : Functions and Graphs

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

• ISBN13: 9780321131966
• ISBN10: 0321131967
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-01-01
• 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

CHAPTER P Prerequisites
P.1 Real Numbers	2	(11)
P.2 Cartesian Coordinate System	13	(10)
P.3 Linear Equations and Inequalities	23	(7)
P.4 Lines In the Plane	30	(14)
P.5 Solving Equations Graphically, Numerically, and Algebraically	44	(9)
P.6 Solving Inequalities Algebraically and Graphically	53	(2)
Key Ideas	55	(2)
Review Exercises	57	(7)
CHAPTER 1 Functions and Graphs
1.1 Modeling and Equation Solving	64	(17)
1.2 Functions and Their Properties	81	(20)
1.3 Twelve Basic Functions	101	(12)
1.4 Building Functions from Functions	113	(18)
1.5 Graphical Transformations	131	(11)
1.6 Modeling with Functions	142	(14)
Math at Work	156	(1)
Key Ideas	156	(1)
Review Exercises	157	(13)
Chapter Project	170
CHAPTER 2 Polynomial, Power, and Rational Functions
2.1 Linear and Quadratic Functions and Modeling	162	(19)
2.2 Power Functions with Modeling	181	(12)
2.3 Polynomial Functions of Higher Degree with Modeling	193	(14)
2.4 Real Zeros of Polynomial Functions	207	(14)
2.5 Complex Numbers	221	(8)
2.6 Complex Zeros and the Fundamental Theorem of Algebra	229	(8)
2.7 Graphs of Rational Functions	237	(12)
2.8 Solving Equations in One Variable	249	(9)
2.9 Solving Inequalities in One Variable	258	(10)
Math at Work	268	(1)
Key Ideas	269	(1)
Review Exercises	270	(4)
Chapter Project	274	(2)
CHAPTER 3 Exponential, Logistic, and Logarithmic Functions
3.1 Exponential and Logistic Functions	276	(14)
3.2 Exponential and Logistic Modeling	290	(10)
3.3 Logarithmic Functions and Their Graphs	300	(10)
3.4 Properties of Logarithmic Functions	310	(10)
3.5 Equation Solving and Modeling	320	(14)
3.6 Mathematics of Finance	334	(11)
Key Ideas	345	(1)
Review Exercises	346	(4)
Chapter Project	350	(2)
CHAPTER 4 Trigonometric Functions
4.1 Angles and Their Measures	352	(10)
4.2 Trigonometric Functions of Acute Angles	362	(10)
4.3 Trigonometry Extended: The Circular Functions	372	(14)
4.4 Graphs of Sine and Cosine: Sinusoids	386	(12)
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant	398	(9)
4.6 Graphs of Composite Trigonometric Functions	407	(9)
4.7 Inverse Trigonometric Functions	416	(10)
4.8 Solving Problems with Trigonometry	426	(12)
Key Ideas	438	(1)
Review Exercises	439	(3)
Chapter Project	442	(2)
CHAPTER 5 Analytic Trigonometry
5.1 Fundamental Identities	444	(10)
5.2 Proving Trigonometric Identities	454	(9)
5.3 Sum and Difference Identities	463	(8)
5.4 Multiple-Angle Identities	471	(7)
5.5 The Law of SInes	478	(9)
5.6 The Law of Cosines	487	(9)
Math at Work	496	(1)
Key Ideas	497	(1)
Review Exercises	497	(3)
Chapter Project	500	(2)
CHAPTER 6 Vectors, Parametric Equations, and Polar Equations
6.1 Vectors in the Plane	502	(12)
6.2 Dot Product of Vectors	514	(8)
6.3 Parametric Equations and Motion	522	(12)
6.4 Polar Coordinates	534	(7)
6.5 Graphs of Polar Equations	541	(9)
6.6 De Moivre's Theorem and nth Roots	550	(10)
Key Ideas	560	(1)
Review Exercises	561	(3)
Chapter Project	564	(2)
CHAPTER 7 Systems and Matrices
7.1 Solving Systems of Two Equations	566	(11)
7.2 Matrix Algebra	577	(15)
7.3 Multivariate Linear Systems and Row Operations	592	(14)
7.4 Partial Fractions	606	(9)
7.5 Systems of Inequalities in Two Variables	615	(8)
Math at Work	623	(1)
Key Ideas	624	(1)
Review Exercises	624	(4)
Chapter Project	628	(2)
CHAPTER 8 Analytic Geometry in Two and Three Dimensions
8.1 Conic Sections and Parabolas	630	(12)
8.2 Ellipses	642	(12)
8.3 Hyperbolas	654	(12)
8.4 Translation and Rotation of Axes	666	(10)
8.5 Polar Equations of Conics	676	(10)
8.6 Three-Dimensional Cartesian Coordinate System	686	(11)
Key Ideas	697	(1)
Review Exercises	697	(3)
Chapter Project	700	(2)
CHAPTER 9 Discrete Mathematics
9.1 Basic Combinatorics	702	(11)
9.2 The Binomial Theorem	713	(6)
9.3 Probability	719	(14)
9.4 Sequences and Series	733	(17)
9.5 Mathematical Induction	750	(8)
9.6 Statistics and Data (Graphical)	758	(13)
9.7 Statistics and Data (Algebraic)	771	(16)
Math at Work	787	(1)
Key Ideas	787	(1)
Review Exercises	788	(4)
Chapter Project	792	(2)
CHAPTER 10 An Introduction to Calculus: Limits, Derivatives, and Integrals
10.1 Limits and Motion: The Tangent Problem	794	(12)
10.2 Limits and Motion: The Area Problem	806	(9)
10.3 More on Limits	815	(14)
10.4 Numerical Derivatives and Integrals	829	(11)
Key Ideas	840	(1)
Review Exercises	840	(2)
Chapter Project	842	(1)
A.1 Radicals and Rational Exponents	843	(5)
A.2 Polynomials and Factoring	848	(8)
A.3 Fractional Expressions	856	(5)
B.1 Formulas from Algebra	861	(1)
B.2 Formulas from Geometry	862	(1)
B.3 Formulas from Trigonometry	863	(1)
B.4 Formulas from Analytic Geometry	864	(2)
B.5 Gallery of Basic Functions	866	(1)
C.1 Logic: An Introduction	867	(6)
C.2 Conditionals and Biconditionals	873	(8)
Glossary	881	(18)
Selected Answers	899	(108)
Applications Index	1007	(4)
Index	1011