Algebra and Trigonometry : Text

by Larson, Ron; Hostetler, Robert P.

• ISBN13: 9780618643219
• ISBN10: 0618643214
• Edition: 7th
• Format: Hardcover
• Copyright: 2006-01-03
• Publisher: Cengage Learning

Summary

This market-leading text continues to provide students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, the new Seventh Edition retains the features that have made Algebra and Trigonometry a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. New! Side-by-side Example Solutions for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles. New! Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, allowing students to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book. New! Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts. Exercise Sets have been carefully analyzed and revised to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications. New! Make a Decision applications--presented throughout the text at the end of selected exercise sets--are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format.Eduspace, powered by Blackboard, Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the College Algebra text. This content is paired with the recognized course management tools of Blackboard. For copyright 2007, two titles have been added to the Precalculus Series: Precalculus with Limits and Precalculus: A Concise Course. These titles enhance the scope of the series, making it even more flexible and adaptable to a variety of learning and teaching styles.

Table of Contents

A Word from the Authors (Preface)	viii
Textbook Features and Highlights	xi
Prerequisites	1	(76)
Review of Real Numbers and Their Properties	2	(10)
Exponents and Radicals	12	(12)
Polynomials and Special Products	24	(9)
Factoring Polynomials	33	(8)
Rational Expressions	41	(10)
Errors and the Algebra of Calculus	51	(7)
The Rectangular Coordinate System and Graphs	58	(19)
Chapter Summary	69	(1)
Review Exercises	70	(3)
Chapter Test	73	(1)
Proofs in Mathematics	74	(1)
P.S. Problem Solving	75	(2)
Equations, Inequalities, and Mathematical Modeling	77	(96)
Graphs of Equations	78	(11)
Linear Equations in One Variable	89	(9)
Modeling with Linear Equations	98	(12)
Quadratic Equations and Applications	110	(16)
Complex Numbers	126	(7)
Other Types of Equations	133	(11)
Linear Inequalities in One Variable	144	(10)
Other Types of Inequalities	154	(19)
Chapter Summary	164	(1)
Review Exercises	165	(4)
Chapter Test	169	(1)
Proofs in Mathematics	170	(1)
P.S. Problem Solving	171	(2)
Functions and Their Graphs	173	(90)
Linear Equations in Two Variables	174	(15)
Functions	189	(14)
Analyzing Graphs of Functions	203	(12)
A Library of Parent Functions	215	(8)
Transformations of Functions	223	(10)
Combinations of Functions: Composite Functions	233	(9)
Inverse Functions	242	(21)
Chapter Summary	252	(1)
Review Exercises	253	(4)
Chapter Test	257	(1)
Cumulative Test: Chapters P--2	258	(2)
Proofs in Mathematics	260	(1)
P.S. Problem Solving	261	(2)
Polynomial Functions	263	(72)
Quadratic Functions and Models	264	(11)
Polynomial Functions of Higher Degree	275	(14)
Polynomial and Synthetic Division	289	(9)
Zeros of Polynomial Functions	298	(15)
Mathematical Modeling and Variation	313	(22)
Chapter Summary	325	(1)
Review Exercises	326	(4)
Chapter Test	330	(1)
Proofs in Mathematics	331	(2)
P.S. Problem Solving	333	(2)
Rational Functions and Conics	335	(48)
Rational Functions and Asymptotes	336	(9)
Graphs of Rational Functions	345	(9)
Conics	354	(13)
Translations of Conics	367	(16)
Chapter Summary	375	(1)
Review Exercises	376	(3)
Chapter Test	379	(1)
Proofs in Mathematics	380	(1)
P.S. Problem Solving	381	(2)
Exponential and Logarithmic Functions	383	(64)
Exponential Functions and Their Graphs	384	(11)
Logarithmic Functions and Their Graphs	395	(10)
Properties of Logarithms	405	(7)
Exponential and Logarithmic Equations	412	(11)
Exponential and Logarithmic Models	423	(24)
Chapter Summary	436	(1)
Review Exercises	437	(4)
Chapter Test	441	(1)
Cumulative Test: Chapters 3--5	442	(2)
Proofs in Mathematics	444	(1)
P.S. Problem Solving	445	(2)
Trigonometry	447	(88)
Angles and Their Measure	448	(12)
Right Triangle Trigonometry	460	(11)
Trigonometric Functions of Any Angle	471	(12)
Graphs of Sine and Cosine Functions	483	(11)
Graphs of Other Trigonometric Functions	494	(11)
Inverse Trigonometric Functions	505	(10)
Applications and Models	515	(20)
Chapter Summary	526	(1)
Review Exercises	527	(4)
Chapter Test	531	(1)
Proofs in Mathematics	532	(1)
P.S. Problem Solving	533	(2)
Analytic Trigonometry	535	(56)
Using Fundamental Identities	536	(8)
Verifying Trigonometric Identities	544	(7)
Solving Trigonometric Equations	551	(11)
Sum and Difference Formulas	562	(7)
Multiple-Angle and Product-to-Sum Formulas	569	(22)
Chapter Summary	581	(1)
Review Exercises	582	(3)
Chapter Test	585	(1)
Proofs in Mathematics	586	(3)
P.S. Problem Solving	589	(2)
Additional Topics in Trigonometry	591	(66)
Law of Sines	592	(9)
Law of Cosines	601	(8)
Vectors in the Plane	609	(13)
Vectors and Dot Products	622	(10)
Trigonometric Form of a Complex Number	632	(25)
Chapter Summary	643	(1)
Review Exercises	644	(4)
Chapter Test	648	(1)
Cumulative Test: Chapters 6--8	649	(2)
Proofs in Mathematics	651	(4)
P.S. Problem Solving	655	(2)
Systems of Equations and Inequalities	657	(76)
Linear and Nonlinear Systems of Equations	658	(11)
Two-Variable Linear Systems	669	(12)
Multivariable Linear Systems	681	(14)
Partial Fractions	695	(8)
Systems of Inequalities	703	(11)
Linear Programming	714	(19)
Chapter Summary	724	(1)
Review Exercises	725	(4)
Chapter Test	729	(1)
Proofs in Mathematics	730	(1)
P.S. Problem Solving	731	(2)
Matrices and Determinants	733	(70)
Matrices and Systems of Equations	734	(15)
Operations with Matrices	749	(15)
The Inverse of a Square Matrix	764	(9)
The Determinant of a Square Matrix	773	(8)
Applications of Matrices and Determinants	781	(22)
Chapter Summary	793	(1)
Review Exercises	794	(5)
Chapter Test	799	(1)
Proofs in Mathematics	800	(1)
P.S. Problem Solving	801	(2)
Sequences, Series, and Probability	803
Sequences and Series	804
Arithmetic Sequences and Partial Sums	815
Geometric Sequences and Series	825
Mathematical Induction	835
The Binomial Theorem	845
Counting Principles	853
Probability	863
Chapter Summary	876
Review Exercises	877
Chapter Test	881
Cumulative Test: Chapters 9--11	882
Proofs in Mathematics	884
P.S. Problem Solving	887
Answers to Odd-Numbered Exercises and Tests	1	(32)
Index	133
Index of Applications (Web: college.hmco.com)
Appendix A Concepts in Statistics (Web: college.hmco.com)
Representing Data
Measures of Central Tendency and Dispersion
Least Squares Regression