College Algebra

by Hirsch, Lewis; Goodman, Arthur

• ISBN13: 9780131433229
• ISBN10: 0131433229
• Edition: 1st
• Format: Hardcover
• Copyright: 1995-02-01
• Publisher: Pearson College Div

Summary

In this text the authors have made a conscientious effort to afford the student every opportunity to look at questions from a variety points of view; to take the time to analyze a problem carefully so that he/she clearly understands what is being asked; to reformulate problems in more familiar terms; and to recognize that most mathematical problems require significantly more thinking and less writing. This text is intended for students who are preparing to take calculus or other courses requiring a similar background.

Table of Contents

Preface to the Instructor	vii
Preface to the Student	xiii
Algebra: The Fundamentals	1	(63)
The Real Numbers	2	(11)
Operations with Real Numbers	13	(7)
Polynomials	20	(14)
Rational Expressions	34	(5)
Exponents and Radicals	39	(16)
The Complex Numbers	55	(9)
Review Exercises	61	(2)
Practice Test	63	(1)
Equations and Inequalities	64	(43)
First-Degree Equations and Inequalities in One Variable	65	(11)
Absolute Value Equations and Inequalities	76	(5)
Quadratic Equations	81	(8)
Radical Equations: Equations Reducible to Quadratic Form	89	(6)
Quadratic and Rational Inequalities	95	(6)
Substitution	101	(6)
Review Exercises	105	(1)
Practice Test	106	(1)
Functions and Graphs: Part I	107	(88)
The Cartesian Coordinate System: Graphing Straight Lines and Circles	108	(17)
Slope	125	(10)
Equations of a Line	135	(11)
Relations and Functions	146	(12)
Function Notation	158	(7)
Relating Equations to Their Graphs	165	(17)
Introduction to Graph Sketching: Symmetry	182	(13)
Summary	189	(3)
Review Exercises	192	(2)
Practice Test	194	(1)
Functions and Graphs: Part II	195	(74)
Basic Graphing Principles	196	(14)
More Graphing Principles: Types of Functions	210	(12)
Extracting Functions from Real-Life Situations	222	(12)
Quadratic Functions	234	(11)
Operations on Functions	245	(7)
Inverse Functions	252	(17)
Summary	262	(3)
Review Exercises	265	(3)
Practice Test	268	(1)
Polynomial, Rational, and Radical Functions	269	(72)
Polynomial Functions	270	(16)
Division of Polynomials and Synthetic Division	286	(5)
Roots of Polynomial Equations: The Remainder Theorem and Factor Theorem	291	(8)
More on the Roots of Polynomial Equations: The Rational Root Theorem and Descartes' Rule of Signs	299	(9)
Rational Functions	308	(13)
Radical Functions	321	(9)
Variation	330	(11)
Summary	336	(3)
Review Exercises	339	(1)
Practice Test	340	(1)
Exponential and Logarithmic Functions	341	(54)
Exponential Functions	342	(12)
Logarithmic Functions	354	(9)
Properties of Logarithms: Logarithmic Equations	363	(6)
Common and Natural Logarithms: Exponential Equations and Change of Base	369	(9)
Applications	378	(17)
Summary	392	(1)
Review Exercises	393	(1)
Practice Test	394	(1)
Systems of Linear Equations and Inequalities	395	(85)
Elimination and Substitution: 2 x 2 Linear Systems	396	(11)
Elimination and Gaussian Elimination: 3 x 3 Linear Systems	407	(8)
Solving Linear Systems Using Augmented Matrices	415	(10)
The Algebra of Matrices	425	(10)
Solving Linear Systems Using Matrix Inverses	435	(10)
Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems	445	(6)
Properties of Determinants	451	(10)
Systems of Linear Inequalities	461	(5)
An Introduction to Linear Programming: Geometric Solutions	466	(14)
Summary	473	(3)
Review Exercises	476	(3)
Practice Test	479	(1)
Conic Sections and Nonlinear Systems	480	(72)
Conic Sections: Circles	481	(4)
The Parabola	485	(14)
The Ellipse	499	(16)
The Hyperbola	515	(16)
Identifying Conic Sections: Degenerate Forms	531	(5)
Nonlinear Systems of Equations and Inequalities	536	(16)
Summary	546	(3)
Review Exercises	549	(2)
Practice Test	551	(1)
Sequence, Series, and Related Topics	552
Sequences	553
Series and Sigma Notation	561
Arithmetic Sequences and Series	567
Geometric Sequences and Series	578
Mathematical Induction	589
Permutations and Combinations	598
The Binomial Theorem	608
Summary	613
Review Exercises	616
Practice Test	617
Tables	T1
Table 1: Exponential Functions	T1
Table 2: Common Logarithms	T2
Table 3: Natural Logarithms	T4
Answers to Selected Exercises	A1
Index	I1