College Algebra Enhanced with Graphing Utilities

by Sullivan, Michael; Sullivan, Michael

• ISBN13: 9780130655929
• ISBN10: 0130655929
• Edition: 3rd
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Prentice Hall

Summary

The Sullivan Enhanced with Graphing Utilities series fully integrates the graphing calculator. These widely adopted books are known for their precise careful presentation of mathematics. This precision permeates the book and is particularly evident in the examples, pedagogy and exercises. This book includes coverage of linear, quadratic, polynomial, rational, exponential and logarithmic functions. In addition, this book discusses the zeros of a polynomial function, systems of equations and inequalities, probability, and conics. For anyone who needs to brush up on everyday or business-related mathematics.

Table of Contents

Preface to the Instructor	xi
Preface to the Student	xvi
List of Applications	xxvii
Photo Credits	xxxiii
Review	1	(88)
Real Numbers	2	(15)
Algebra Review	17	(8)
Geometry Review	25	(5)
Integer Exponents	30	(9)
Polynomials	39	(11)
Factoring Polynomials	50	(9)
Rational Expressions	59	(12)
Square Roots; Radicals	71	(8)
Rational Exponents	79	(10)
Chapter Review	84	(5)
Graphs	89	(106)
Rectangular Coordinates; Graphing Utilities	90	(10)
Introduction to Graphing Equations	100	(9)
Solving Equations Using a Graphing Utility; Linear and Quadratic Equations	109	(18)
Setting Up Equations; Applications	127	(15)
Radical Equations; Equations Quadratic in Form; Absolute Value Equations	142	(7)
Solving Inequalities	149	(14)
Lines	163	(17)
Circles	180	(15)
Chapter Review	186	(6)
Chapter Projects	192	(3)
Linear and Quadratic Functions	195	(60)
Functions	196	(19)
Linear Functions and Models	215	(11)
Quadratic Functions	226	(11)
Quadratic Models	237	(18)
Chapter Review	248	(4)
Chapter Projects	252	(1)
Cumulative Review	252	(3)
Functions and Their Graphs	255	(68)
Symmetry; Graphing Key Equations	256	(7)
Properties of Functions	263	(13)
Library of Functions; Piecewise-Defined Functions	276	(10)
Graphing Techinques: Transformations	286	(13)
Operations on Functions; Composite Functions	299	(10)
Mathematical Models: Constructing Functions	309	(14)
Chapter Review	317	(3)
Chapter Projects	320	(1)
Cumulative Review	321	(2)
Polynomial and Rational Functions	323	(56)
Power Functions and Models	324	(6)
Polynomial Functions and Models	330	(13)
Rational Functions I	343	(12)
Rational Functions II: Analyzing Graphs	355	(10)
Polynomial and Rational Inequalities	365	(14)
Chapter Review	373	(3)
Chapter Projects	376	(1)
Cumulative Review	377	(2)
The Zeros of a Polynomial Function	379	(38)
Synthetic Division	380	(4)
The Real Zeros of a Polynomial Function	384	(14)
Complex Numbers; Quadratic Equations with a Negative Discriminant	398	(9)
Complex Zeros; Fundamental Theorem of Algebra	407	(10)
Chapter Review	412	(2)
Chapter Projects	414	(2)
Cumulative Review	416	(1)
Exponential and Logarithmic Functions	417	(94)
One-to-One Functions: Inverse Functions	418	(13)
Exponential Functions	431	(14)
Logarithmic Functions	445	(12)
Properties of Logarithms	457	(10)
Logarithmic and Exponential Equations	467	(4)
Compound Interest	471	(11)
Growth and Decay	482	(11)
Exponential, Logarithmic, and Logistic Models	493	(18)
Chapter Review	502	(6)
Chapter Projects	508	(2)
Cumulative Review	510	(1)
Systems of Equations And Inequalities	511	(98)
Systems of Linear Equations: Two Equations Containing Two Variables	512	(11)
Systems of Linear Equations: Three Equations Containing Three Variables	523	(6)
Systems of Linear Equations: Matrices	529	(18)
Systems of Linear Equations: Determinants	547	(12)
Matrix Algebra	559	(18)
Systems of Linear Inequalities; Linear Programming	577	(16)
Partial Fraction Decomposition	593	(16)
Chapter Review	601	(5)
Chapter Projects	606	(1)
Cumulative Review	607	(2)
Sequences; Induction; The Binomial Theorem	609	(50)
Sequences	610	(15)
Arithmetic Sequences	625	(6)
Geometric Sequences; Geometric Series	631	(11)
Mathematical Induction	642	(4)
The Binomial Theorem	646	(13)
Chapter Review	654	(3)
Chapter Projects	657	(1)
Cumulative Review	658	(1)
Counting and Probability	659	(42)
Sets and Counting	660	(6)
Permutations and Combinations	666	(11)
Probability of Equally Likely Outcomes	677	(13)
Obtaining Probabilities from Data	690	(11)
Chapter Review	695	(4)
Chapter Projects	699	(1)
Cumulative Review	700	(1)
Conics	701	(1)
Preliminaries	702	(1)
The Parabola	703	(12)
The Ellipse	715	(12)
The Hyperbola	727	(15)
Systems of Nonlinear Equations	742	(11)
Chapter Review	753	(3)
Chapter Projects	756	(1)
Cumulative Review	757
Answers	1	(1)
Index	1

Excerpts

As professors at both an urban public university and a community college, Michael Sullivan and Michael Sullivan, III are aware of the varied needs of College Algebra students, ranging from those who have little mathematical background and a fear of mathematics courses, to those having a strong mathematical education and a high level of motivation. For some of your students, this will be their last course in mathematics, while others will further their mathematical education. This text is written for both groups. As a teacher, and as an author of precalculus, engineering calculus, finite math, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the coauthor, he also understands the realities of college life. His co-author and son, Michael Sullivan III, believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Together, both authors have taken great pains to ensure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style. We encourage you to share with us your experiences teaching from this text. In the Third Edition The third edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. One important benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used previous editions. This feedback has proved invaluable and has been used to make changes that improve the flow, usability, and accessibility of the text. For example, some topics have been moved to better reflect the way teachers approach the course and problems have been added where more practice was needed. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components. Reorganized Content for College Algebra Appendix Review Now expanded, this material appears in the beginning of the book as Chapter R Chapter 1 Scatter diagrams now appear in Section 2.2 Linear Functions and Models Section 1.2 has been split into two sections. In 3/e Section 1.2 contains point plotting, graphing equations on a graphing utility, and intercepts. Section 3.1 covers symmetry and graphing key equations. This adheres to the "just in time approach" by placing symmetry and key equations closer to functions. Section 1.3 from 2/e has been split into two sections--1.3 and 1.5. Section 1.5 has been expanded to include quadratic-in-form equations. Chapter 2 Section 2.2 now includes the discussion on scatter diagrams. Quadratic equations now appears earlier as part of Section 1.3. Chapter 3 Section 3.1 contains the discussion on symmetry and graphing key equations. Section 3.1 from 2/e is now two sections: Section 3.2 covers properties of functions, while Section 3.3 covers the library of functions and piecewise-defined functions. Chapter 4 This chapter contains Sections 4.1, 4.2, 4.7 and 4.8 from 2/e. The section on rational functions has been split into two sections to accommodate a single lecture for each section. Chapter 5 This chapter contains the remaining sections of Chapter 4 from 2/e. Chapter 6 (Formerly Chapter 5) Section 6.2 now includes a discussion of basic exponential equat