Precalculus Through Modeling and Visualization

by Rockswold, Gary K.; Hornsby, John; Lial, Margaret L.

• ISBN13: 9780321057778
• ISBN10: 0321057775
• Format: Hardcover
• Copyright: 1999-08-01
• Publisher: Pearson College Div

Table of Contents

Preface	ix
Introduction to Functions and Graphs	1	(100)
Data, Numbers, and Algorithms	2	(12)
Visualization of Data	14	(12)
Checking Basic Concepts for Sections 1.1 and 1.2	26	(1)
Functions and Their Representations	26	(17)
Types of Functions and Their Rates of Change	43	(20)
Checking Basic Concepts for Sections 1.3 and 1.4	63	(1)
Modeling Data with Functions	63	(13)
Transformations of Graphs	76	(25)
Checking Basic Concepts for Sections 1.5 and 1.6	95	(1)
Summary	95	(1)
Review Exercises	96	(3)
Extended and Discovery Exercises	99	(2)
Linear Functions and Equations	101	(81)
Linear Equations	102	(14)
Linear Inequalities	116	(15)
Checking Basic Concepts for Sections 2.1 and 2.2	131	(1)
Equations of Lines	131	(16)
Piecewise-Defined Functions	147	(16)
Checking Basic Concepts for Sections 2.3 and 2.4	163	(1)
Linear Approximation	163	(19)
Checking Basic Concepts for Section 2.5	176	(1)
Summary	176	(1)
Review Exercises	177	(3)
Extended and Discovery Exercises	180	(2)
Nonlinear Functions and Equations	182	(114)
Quadratic Equations and Inequalities	183	(17)
Nonlinear Functions and Their Graphs	200	(19)
Checking Basic Concepts for Sections 3.1 and 3.2	219	(1)
Polynomial Functions and Their Graphs	219	(20)
Real Zeros of Polynomial Functions	239	(16)
Checking Basic Concepts for Sections 3.3 and 3.4	255	(1)
The Fundamental Theorem of Algebra	255	(13)
Rational Functions	268	(28)
Checking Basic Concepts for Sections 3.5 and 3.6	288	(1)
Summary	289	(1)
Review Exercises	290	(3)
Extended and Discovery Exercises	293	(3)
Inverse Functions	296	(90)
Combining Functions	297	(17)
Inverse Functions and Their Representations	314	(17)
Checking Basic Concepts for Sections 4.1 and 4.2	331	(1)
Exponential Functions	331	(16)
Logarithmic Functions	347	(19)
Checking Basic Concepts for Sections 4.3 and 4.4	366	(1)
Exponential and Logarithmic Equations	366	(20)
Checking Basic Concepts for Section 4.5	379	(1)
Summary	380	(1)
Review Exercises	380	(4)
Extended and Discovery Exercises	384	(2)
Trigonometric Functions	386	(105)
Angles and their Measure	387	(15)
Right Triangle Trigonometry	402	(15)
Checking Basic Concepts for Sections 5.1 and 5.2	417	(1)
The Sine and Cosine Functions and Their Graphs	417	(17)
Other Trigonometric Functions and Their Graphs	434	(16)
Checking Basic Concepts for Sections 5.3 and 5.4	450	(1)
Modeling with Trigonometric Functions	450	(18)
Inverse Trigonometric Functions	468	(23)
Checking Basic Concepts for Sections 5.5 and 5.6	484	(1)
Summary	485	(1)
Review Exercises	486	(3)
Extended and Discovery Exercises	489	(2)
Trigonometric Identities and Equations	491	(71)
Fundamental Identities	492	(14)
Verifying Identities	506	(10)
Checking Basic Concepts for Sections 6.1 and 6.2	516	(1)
Trigonometric Equations	516	(14)
Sum and Difference Identities	530	(12)
Checking Basic Concepts for Sections 6.3 and 6.4	542	(1)
Multiple-Angle Identities	542	(20)
Checking Basic Concepts for Section 6.5	557	(1)
Summary	557	(1)
Review Exercises	558	(2)
Extended and Discovery Exercises	560	(2)
Further Topics in Trigonometry	562	(72)
Law of Sines	563	(11)
Law of Cosines	574	(10)
Checking Basic Concepts for Sections 7.1 and 7.2	584	(1)
Vectors	584	(16)
Parametric Equations	600	(8)
Checking Basic Concepts for Sections 7.3 and 7.4	608	(1)
Polar Equations	608	(10)
Trigonometric Form and Roots of Complex Numbers	618	(16)
Checking Basic Concepts for Sections 7.5 and 7.6	628	(1)
Summary	628	(1)
Review Exercises	629	(3)
Extended and Discovery Exercises	632	(2)
Systems of Equations and Inequalities	634	(94)
Functions and Equations of More than One Variable	635	(14)
Linear Systems of Equations and Inequalities in Two Variables	649	(19)
Checking Basic Concepts for Sections 8.1 and 8.2	668	(1)
Solutions of Linear Systems Using Matrices	668	(14)
Properties and Applications of Matrices	682	(15)
Checking Basic Concepts for Sections 8.3 and 8.4	697	(1)
Inverses of Matrices	697	(13)
Determinants	710	(18)
Checking Basic Concepts for Sections 8.5 and 8.6	720	(1)
Summary	721	(1)
Review Exercises	721	(4)
Extended and Discovery Exercises	725	(3)
Further Topics in Algebra	728	(80)
Sequences	729	(14)
Series	743	(14)
Checking Basic Concepts for Sections 9.1 and 9.2	757	(1)
Conic Sections	757	(23)
Checking Basic Concepts for Section 9.3	779	(1)
Counting	780	(12)
Probability	792	(16)
Checking Basic Concepts for Sections 9.4 and 9.5	803	(1)
Summary	804	(1)
Review Exercises	805	(2)
Extended and Discovery Exercises	807	(1)
Bibliography	808
Answers to Selected Exercises	A-1	(1)
Index of Applications	I-1	(1)
Index	I-7