Precalculus Functions and Graphs A Graphing Approach

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

• ISBN13: 9780618394760
• ISBN10: 0618394761
• Edition: 4th
• Format: Hardcover
• Copyright: 2004-03-08
• Publisher: Brooks Cole

Summary

As part of the market-leadingGraphing ApproachSeries by Larson, Hostetler, and Edwards,Precalculus Functions and Graphs: 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 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. TheLibrary of Functionsthread 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. ALibrary of Functions Summaryalso appears inside the front cover for quick reference. Technology Supportnotes provided at point-of-use throughout the text guide students to theTechnology 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 theGraphing Technology Guideon the textbook web site for keystroke support. Houghton Mifflin'sEduspaceonline classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.

Table of Contents

A Word from the Authors (Preface)	viii
Features Highlights	xii
Functions and Their Graphs	1	(86)
Introduction to Library of Functions	2	(1)
Lines in the Plane	3	(13)
Functions	16	(14)
Graphs of Functions	30	(12)
Shifting, Reflecting, and Stretching Graphs	42	(9)
Combinations of Functions	51	(11)
Inverse Functions	62	(10)
Exploring Data: Linear Models and Scatter Plots	72	(15)
Chapter Summary	81	(1)
Review Exercises	82	(4)
Chapter Test	86	(1)
Polynomial and Rational Functions	87	(88)
Quadratic Functions	88	(11)
Polynomial Functions of Higher Degree	99	(13)
Real Zeros of Polynomial Functions	112	(15)
Complex Numbers	127	(8)
The Fundamental Theorem of Algebra	135	(7)
Rational Functions and Asymptotes	142	(10)
Graphs of Rational Functions	152	(9)
Exploring Data: Quadratic Models	161	(14)
Chapter Summary	168	(1)
Review Exercises	169	(5)
Chapter Test	174	(1)
Exponential and Logarithmic Functions	175	(72)
Exponential Functions and Their Graphs	176	(12)
Logarithmic Functions and Their Graphs	188	(11)
Properties of Logarithms	199	(7)
Solving Exponential and Logarithmic Equations	206	(11)
Exponential and Logarithmic Models	217	(12)
Exploring Data: Nonlinear Models	229	(18)
Chapter Summary	238	(1)
Review Exercises	239	(5)
Chapter Test	244	(1)
Cumulative Test: Chapters 1--3	245	(2)
Trigonometric Functions	247	(92)
Radian and Degree Measure	248	(11)
Trigonometric Functions: The Unit Circle	259	(8)
Right Triangle Trigonometry	267	(11)
Trigonometric Functions of Any Angle	278	(9)
Graphs of Sine and Cosine Functions	287	(11)
Graphs of Other Trigonometric Functions	298	(11)
Inverse Trigonometric Functions	309	(11)
Applications and Models	320	(19)
Chapter Summary	332	(1)
Review Exercises	333	(5)
Chapter Test	338	(1)
Analytic Trigonometry	339	(52)
Using Fundamental Identities	340	(8)
Verifying Trigonometric Identities	348	(8)
Solving Trigonometric Equations	356	(12)
Sum and Difference Formulas	368	(7)
Multiple-Angle and Product-to-Sum Formulas	375	(16)
Chapter Summary	386	(1)
Review Exercises	387	(3)
Chapter Test	390	(1)
Additional Topics in Trigonometry	391	(60)
Law of Sines	392	(9)
Law of Cosines	401	(7)
Vectors in the Plane	408	(14)
Vectors and Dot Products	422	(10)
Trigonometric Form of a Complex Number	432	(19)
Chapter Summary	443	(1)
Review Exercises	444	(4)
Chapter Test	448	(1)
Cumulative Test: Chapters 4--6	449	(2)
Linear Systems and Matrices	451	(104)
Solving Systems of Equations	452	(11)
Systems of Linear Equations in Two Variables	463	(10)
Multivariable Linear Systems	473	(16)
Matrices and Systems of Equations	489	(15)
Operations with Matrices	504	(15)
The Inverse of a Square Matrix	519	(9)
The Determinant of a Square Matrix	528	(8)
Applications of Matrices and Determinants	536	(19)
Chapter Summary	546	(2)
Review Exercises	548	(6)
Chapter Test	554	(1)
Sequences, Series, and Probability	555	(76)
Sequences and Series	556	(11)
Arithmetic Sequences and Partial Sums	567	(9)
Geometric Sequences and Series	576	(10)
Mathematical Induction	586	(8)
The Binomial Theorem	594	(8)
Counting Principles	602	(10)
Probability	612	(19)
Chapter Summary	625	(1)
Review Exercises	626	(4)
Chapter Test	630	(1)
Topics in Analytic Geometry	631
Introduction to Conies: Parabolas	632	(8)
Ellipses	640	(9)
Hyperbolas	649	(10)
Rotation and Systems of Quadratic Equations	659	(9)
Parametric Equations	668	(8)
Polar Coordinates	676	(6)
Graphs of Polar Equations	682	(9)
Polar Equations of Conies	691
Chapter Summary	698	(1)
Review Exercises	699	(4)
Chapter Test	703	(1)
Cumulative Test: Chapters 7--9	704
Appendices
Appendix A Technology Support Guide	1	(24)
Appendix B Review of Graphs, Equations, and Inequalities	25	(59)
The Cartesian Plane	25	(11)
Graphs of Equations	36	(11)
Solving Equations Algebraically and Graphically	47	(16)
Solving Inequalities Algebraically and Graphically	63	(12)
Exploring Data: Representing Data Graphically	75	(9)
Appendix C Proofs of Selected Theorems	84	(14)
Appendix D Concepts in Statistics	98	(11)
Measures of Central Tendency and Dispersion	98	(9)
Least Squares Regression	107	(2)
Appendix E Solving Linear Equations and Inequalities	109	(3)
Appendix F Systems of Inequalities	112	(19)
Solving Systems of Inequalities	112	(10)
Linear Programming	122	(9)
Answers to Odd-Numbered Exercises and Tests	131	(130)
Index of Applications	261	(4)
Index	265