Essentials of College Algebra

by Lial, Margaret L.; Hornsby, John; Schneider, David I.

• ISBN13: 9780321385239
• ISBN10: 0321385233
• Edition: 1st
• Format: Paperback
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

Focused on helping students develop both the conceptual understanding and the analytical skills necessary to experiencesuccess in mathematics, the authors present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. The book addresses the diverse needs of today's students through an open design, current figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids.

Table of Contents

Preface	vii
Supplements Guide	xi
R Review of Basic Concepts	1	(532)
Real Numbers and Their Properties	2	(14)
Sets of Numbers and the Number Line
Exponents
Order of Operations
Properties of Real Numbers
Order and Absolute Value	16	(8)
Order on the Number Line
Absolute Value
Properties of Absolute Value
Polynomials	24	(13)
Rules for Exponents
Polynomials
Addition and Subtraction
Multiplication
Division
Factoring Polynomials	37	(9)
Factoring Out the Greatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring Binomials
Factoring by Substitution
Rational Expressions	46	(9)
Rational Expressions
Lowest Terms of a Rational Expression
Multiplication and Division
Addition and Subtraction
Complex Fractions
Rational Exponents	55	(10)
Negative Exponents and the Quotient Rule
Rational Exponents
Complex Fractions Revisited
Radical Expressions	65	(20)
Radical Notation
Simplified Radicals
Operations with Radicals
Rationalizing Denominators
Summary	76	(3)
Review Exercises	79	(4)
Test	83	(1)
Quantitative Reasoning	84	(1)
Equations and Inequalities	85	(96)
Linear Equations	86	(6)
Basic Terminology of Equations
Solving Linear Equations
Identities, Conditional Equations, and Contradictions
Solving for a Specified Variable (Literal Equations)
Applications and Modeling with Linear Equations	92	(15)
Solving Applied Problems
Geometry Problems
Motion Problems
Work Rate Problems
Mixture Problems
Modeling with Linear Equations
Complex Numbers	107	(8)
Basic Concepts of Complex Numbers
Operations on Complex Numbers
Quadratic Equations	115	(10)
Solving a Quadratic Equation
Completing the Square
The Quadratic Formula
Solving for a Specified Variable
The Discriminant
Applications and Modeling with Quadratic Equations	125	(11)
Geometry Problems
Using the Pythagorean Theorem
Height of a Propelled Object
Modeling with Quadratic Equations
Other Types of Equations	136	(10)
Rational Equations
Equations with Radicals
Equations Quadratic in Form
Summary Exercises on Solving Equations	146	(1)
Inequalities	146	(14)
Linear Inequalities
Three-Part Inequalities
Quadratic Inequalities
Rational Inequalities
Absolute Value Equations and Inequalities	160	(21)
Absolute Value Equations
Absolute Value Inequalities
Special Cases Absolute Value Models for Distance and Tolerance
Summary	167	(4)
Review Exercises	171	(7)
Test	178	(2)
Quantitative Reasoning	180	(1)
Graphs and Functions	181	(112)
Graphs of Equations	182	(15)
Ordered Pairs
The Rectangular Coordinate System
The Distance Formula
The Midpoint Formula
Graphing Equations
Circles
Functions	197	(17)
Relations and Functions
Domain and Range
Determining Functions from Graphs or Equations
Function Notation
Increasing, Decreasing, and Constant Functions
Linear Functions	214	(13)
Graphing Linear Functions
Standard Form Ax + By = C
Slope
Average Rate of Change
Linear Models
Equations of Lines; Curve Fitting	227	(15)
Point-Slope Form
Slope-Intercept Form
Vertical and Horizontal Lines
Parallel and Perpendicular Lines
Modeling Data
Solving Linear Equations in One Variable by Graphing
Summary Exercises on Graphs, Functions, and Equations	241	(1)
Graphs of Basic Functions	242	(11)
Continuity
The Identity, Squaring, and Cubing Functions
The Square Root and Cube Root Functions
The Absolute Value Function
Piecewise-Defined Functions
The Relation x = y2
Graphing Techniques	253	(15)
Stretching and Shrinking
Reflecting
Symmetry
Even and Odd Functions
Translations
Function Operations and Composition	268	(25)
Arithmetic Operations on Functions
The Difference Quotient
Composition of Functions
Summary	281	(4)
Review Exercises	285	(5)
Test	290	(2)
Quantitative Reasoning	292	(1)
Polynomial and Rational Functions	293	(96)
Quadratic Functions and Models	294	(19)
Quadratic Functions
Graphing Techniques
Completing the Square
The Vertex Formula
Quadratic Models and Curve Fitting
Synthetic Division	313	(7)
Synthetic Division
Evaluating Polynomial Functions Using the Remainder Theorem
Testing Potential Zeros
Zeros of Polynomial Functions	320	(11)
Factor Theorem
Rational Zeros Theorem
Number of Zeros
Conjugate Zeros Theorem
Finding Zeros of a Polynomial Function
Descartes' Rule of Signs
Polynomial Functions: Graphs, Applications, and Models	331	(19)
Graphs of f(x) = axn
Graphs of General Polynomial Functions
Turning Points and End Behavior
Graphing Techniques
Intermediate Value and Boundedness Theorems
Approximating Real Zeros
Polynomial Models and Curve Fitting
Summary Exercises on Polynomial Functions, Zeros, and Graphs	349	(1)
Rational Functions: Graphs, Applications, and Models	350	(18)
The Reciprocal Function f(x) = 1/x
The Function f(x) =
Asymptotes
Steps for Graphing Rational Functions
Rational Function Models
Variation	368	(21)
Direct Variation
Inverse Variation
Combined and Joint Variation
Summary	377	(4)
Review Exercises	381	(5)
Test	386	(2)
Quantitative Reasoning	388	(1)
Exponential and Logarithmic Functions	389	(84)
Inverse Functions	390	(12)
Inverse Operations
One-to-One Functions
Inverse Functions
Equations of Inverses
An Application of Inverse Functions to Cryptography
Exponential Functions	402	(16)
Exponents and Properties
Exponential Functions
Exponential Equations
Compound Interest
The Number e and Continuous Compounding
Exponential Models and Curve Fitting
Logarithmic Functions	418	(14)
Logarithms
Logarithmic Equations
Logarithmic Functions
Properties of Logarithms
Summary Exercises on Inverse, Exponential, and Logarithmic Functions	431	(1)
Evaluating Logarithms and the Change-of-Base Theorem	432	(11)
Common Logarithms
Applications and Modeling with Common Logarithms
Natural Logarithms
Applications and Modeling with Natural Logarithms
Logarithms to Other Bases
Exponential and Logarithmic Equations	443	(9)
Exponential Equations
Logarithmic Equations
Applications and Modeling
Applications and Models of Exponential Growth and Decay	452	(21)
The Exponential Growth or Decay Function
Growth Function Models
Decay Function Models
Summary	464	(3)
Review Exercises	467	(4)
Test	471	(1)
Quantitative Reasoning	472	(1)
Other Topics in Algebra	473	(60)
Systems of Linear Equations	474	(18)
Linear Systems
Substitution Method
Elimination Method
Special Systems
Applying Systems of Equations
Solving Linear Systems with Three Unknowns (Variables)
Using Systems of Equations to Model Data
Summary Exercises on Systems of Equations	491	(1)
Sequences and Series	492	(11)
Sequences
Series and Summation Notation
Summation Properties
Arithmetic Sequences and Series	503	(9)
Arithmetic Sequences
Arithmetic Series
Geometric Sequences and Series	512	(21)
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Summary Exercises on Sequences and Series	523	(2)
Summary	525	(3)
Review Exercises	528	(3)
Test	531	(1)
Quantitative Reasoning	532	(1)
Appendix Sets	533	(6)
Glossary	539
Solutions to Selected Exercises	1	(1)
Answers to Selected Exercises	1	(1)
Index of Applications	1	(4)
Index	5