Precalculus : A Graphing Approach

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618394661
• ISBN10: 0618394664
• Edition: 4th
• Format: Hardcover
• Copyright: 2004-01-15
• Publisher: Brooks Cole

Summary

As part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This new edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills. Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles. New! The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference. New! Technology Support notes provided at point-of-use throughout the text guide students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystroke support. New! Technology Tips, also provided at point-of-use, call attention to the strengths and weaknesses of graphing technology. Some of these tips offer alternative methods for solving or checking a problem using technology. New! Because students are often misled by the jagged nature of graphs generated by graphing calculators, this text frequently highlights the path of a function in color on the calculator image. This unique design feature enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings. Study Tips at point-of-use throughout the text reinforce concepts and help students learn how to study mathematics. New! Checkpoint questions appear after each worked-out solution, directing students to work a similar exercise for further practice or concept reinforcement. These can be used by instructors in class to quickly check student understanding or by students to practice and study concepts. Chapter Review exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and help them to develop strong study- and test-taking skills. The Student Success Organizer is a valuable note-taking guide that helps students organize their class notes and create an effective study and review tool. New! Text-specific Tutorial Support is provided in numerous additional resources designed to help students succeed. These resources include live online tutoring, instructional DVDs and videos, and algorithmic tutorial support and self-assessment available on CD-ROM and the web. Explorations provided at point-of-use throughout the text can help instructors provide a quick introduction to concepts or reinforce student understanding. <

Table of Contents

A Word from the Authors (Preface)	vi
Features Highlights	x
Prerequisites	1	(72)
Real Numbers	2	(10)
Exponents and Radicals	12	(12)
Polynomials and Factoring	24	(13)
Rational Expressions	37	(10)
The Cartesian Plane	47	(11)
Exploring Data: Representing Data Graphically	58	(15)
Chapter Summary	67	(1)
Review Exercises	68	(4)
Chapter Test	72	(1)
Functions and Their Graphs	73	(88)
Introduction to Library of Functions	74	(1)
Graphs of Equations	75	(11)
Lines in the Plane	86	(13)
Functions	99	(14)
Graphs of Functions	113	(12)
Shifting, Reflecting, and Stretching Graphs	125	(9)
Combinations of Functions	134	(11)
Inverse Functions	145	(16)
Chapter Summary	155	(1)
Review Exercises	156	(4)
Chapter Test	160	(1)
Solving Equations and Inequalities	161	(78)
Linear Equations and Problem Solving	162	(10)
Solving Equations Graphically	172	(11)
Complex Numbers	183	(8)
Solving Equations Algebraically	191	(19)
Solving Inequalities Algebraically and Graphically	210	(12)
Exploring Data: Linear Models and Scatter Plots	222	(17)
Chapter Summary	231	(1)
Review Exercises	232	(4)
Chapter Test	236	(1)
Cumulative Test: Chapters P-2	237	(2)
Polynomial and Rational Functions	239	(80)
Quadratic Functions	240	(11)
Polynomial Functions of Higher Degree	251	(13)
Real Zeros of Polynomial Functions	264	(15)
The Fundamental Theorem of Algebra	279	(7)
Rational Functions and Asymptotes	286	(10)
Graphs of Rational Functions	296	(9)
Exploring Data: Quadratic Models	305	(14)
Chapter Summary	312	(1)
Review Exercises	313	(5)
Chapter Test	318	(1)
Exponential and Logarithmic Functions	319	(72)
Exponential Functions and Their Graphs	320	(12)
Logarithmic Functions and Their Graphs	332	(11)
Properties of Logarithms	343	(7)
Solving Exponential and Logarithmic Equations	350	(11)
Exponential and Logarithmic Models	361	(12)
Exploring Data: Nonlinear Models	373	(18)
Chapter Summary	382	(1)
Review Exercises	383	(5)
Chapter Test	388	(1)
Cumulative Test: Chapters 3-4	389	(2)
Trigonometric Functions	391	(88)
Angles and Their Measure	392	(11)
Right Triangle Trigonometry	403	(11)
Trigonometric Functions of Any Angle	414	(13)
Graphs of Sine and Cosine Functions	427	(11)
Graphs of Other Trigonometric Functions	438	(11)
Inverse Trigonometric Functions	449	(11)
Applications and Models	460	(19)
Chapter Summary	472	(1)
Review Exercises	473	(5)
Chapter Test	478	(1)
Analytic Trigonometry	479	(52)
Using Fundamental Identities	480	(8)
Verifying Trigonometric Identities	488	(8)
Solving Trigonometric Equations	496	(12)
Sum and Difference Formulas	508	(7)
Multiple-Angle and Product-to-Sum Formulas	515	(16)
Chapter Summary	526	(1)
Review Exercises	527	(3)
Chapter Test	530	(1)
Additional Topics in Trigonometry	531	(60)
Law of Sines	532	(9)
Law of Cosines	541	(7)
Vectors in the Plane	548	(14)
Vectors and Dot Products	562	(10)
Trigonometric Form of a Complex Number	572	(19)
Chapter Summary	583	(1)
Review Exercises	584	(4)
Chapter Test	588	(1)
Cumulative Test: Chapters 5-7	589	(2)
Linear Systems and Matrices	591	(104)
Solving Systems of Equations	592	(11)
Systems of Linear Equations in Two Variables	603	(10)
Multivariable Linear Systems	613	(16)
Matrices and Systems of Equations	629	(15)
Operations with Matrices	644	(15)
The Inverse of a Square Matrix	659	(9)
The Determinant of a Square Matrix	668	(8)
Applications of Matrices and Determinants	676	(19)
Chapter Summary	686	(2)
Review Exercises	688	(6)
Chapter Test	694	(1)
Sequences, Series, and Probability	695	(76)
Sequences and Series	696	(11)
Arithmetic Sequences and Partial Sums	707	(9)
Geometric Sequences and Series	716	(10)
Mathematical Induction	726	(8)
The Binomial Theorem	734	(8)
Counting Principles	742	(10)
Probability	752	(19)
Chapter Summary	765	(1)
Review Exercises	766	(4)
Chapter Test	770	(1)
Topics in Analytic Geometry	771
Conics	772	(14)
Translations of Conics	786	(9)
Parametric Equations	795	(8)
Polar Coordinates	803	(6)
Graphs of Polar Equations	809	(9)
Polar Equations of Conics	818
Chapter Summary	825	(1)
Review Exercises	826	(4)
Chapter Test	830	(1)
Cumulative Test: Chapters 8-10	831
Appendices
Appendix A Technology Support Guide	1	(24)
Appendix B Proofs of Selected Theorems	25	(13)
Appendix C Concepts in Statistics	38	(11)
C.1 Measures of Central Tendency and Dispersion	38	(47)
C.2 Least Squares Regression	47	(49)
Appendix D Solving Linear Equations and Inequalities	49	(3)
Appendix E Systems of Inequalities	52	(19)
E.1 Solving Systems of Inequalities	52	(10)
E.2 Linear Programming	62	(71)
Answers to Odd-Numbered Exercises and Tests	71	(140)
Index of Applications	211	(4)
Index	215