College Algebra

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

• ISBN13: 9780321227577
• ISBN10: 0321227573
• Edition: 9th
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Addison Wesley

Summary

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students planning to continue their study of mathematics in calculus, trigonometry, statistics, or other disciplines, as well as those taking college algebra as their final mathematics course, will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

Table of Contents

Preface	viii
Supplements Guide	xii
R Review of Basic Concepts	1	(84)
R.1 Real Numbers and Their Properties	2	(14)
Sets of Numbers and the Number Line
Exponents
Order of Operations
Properties of Real Numbers
R.2 Order and Absolute Value	16	(8)
Order on the Number Line
Absolute Value
Properties of Absolute Value
R.3 Polynomials	24	(13)
Rules for Exponents
Polynomials
Addition and Subtraction
Multiplication
Division
R.4 Factoring Polynomials	37	(9)
Factoring Out the Greatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring Binomials
Factoring by Substitution
R.5 Rational Expressions	46	(9)
Rational Expressions
Lowest Terms of a Rational Expression
Multiplication and Division
Addition and Subtraction
Complex Fractions
R.6 Rational Exponents	55	(10)
Negative Exponents and the Quotient Rule
Rational Exponents
Complex Fractions Revisited
R.7 Radical Expressions	65	(11)
Radical Notation
Simplified Radicals
Operations with Radicals
Rationalizing Denominators
Summary	76	(3)
Review Exercises	79	(4)
Test	83	(1)
Quantitative Reasoning	84	(1)
1 Equations and Inequalities	85	(96)
1.1 Linear Equations	86	(6)
Basic Terminology of Equations
Solving Linear Equations
Identities, Conditional Equations, and Contradictions
Solving, for a Specified Variable (Literal Equations)
1.2 Applications and Modeling with Linear Equations	92	(15)
Solving Applied Problems
Geometry Problems
Motion Problems
Work Rate Problems
Mixture Problems
Modeling with Linear Equations
1.3 Complex Numbers	107	(8)
Basic Concepts of Complex Numbers
Operations on Complex Numbers
1 .4 Quadratic Equations	115	(10)
Solving a Quadratic Equation
Completing the Square
The Quadratic Formula
Solving for a Specified Variable
The Discriminant
1.5 Applications and Modeling with Quadratic Equations	125	(11)
Geometry Problems
Using the Pythagorean Theorem
Height of a Propelled Object
Modeling with Quadratic Equations
1.6 Other Types of Equations	136	(10)
Rational Equations
Equations with Radicals
Equations Quadratic in Form
Summary Exercises on Solving Equations	146	(1)
1.7 Inequalities	146	(14)
Linear Inequalities
Three-Part Inequalities
Quadratic Inequalities
Rational Inequalities
1.8 Absolute Value Equations and Inequalities	160	(7)
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)
2 Graphs and Functions	181	(112)
2.1 Graphs of Equations	182	(15)
Ordered Pairs
The Rectangular Coordinate System
The Distance Formula
The Midpoint Formula
Graphing Equations
Circles
2.2 Functions	197	(17)
Relations and Functions
Domain and Range
Determining Functions from Graphs or Equations
Function Notation
Increasing, Decreasing, and Constant Functions
2.3 Linear Functions	214	(13)
Graphing Linear Functions
Standard Form Ax + By = C
Slope
Average Rate of Change
Linear Models
2.4 Equations of Lines; Curve Fitting	227	(14)
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)
2.5 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
2.6 Graphing Techniques	253	(15)
Stretching and Shrinking
Reflecting
Symmetry
Even and Odd Functions
Translations
2.7 Function Operations and Composition	268	(13)
Arithmetic Operations on Functions
The Difference Quotient
Composition of Functions
Summary	281	(4)
Review Exercises	285	(5)
Test	290	(2)
Quantitative Reasoning	292	(1)
3 Polynomial and Rational Functions	293	(96)
3.1 Quadratic Functions and Models	294	(19)
Quadratic Functions
Graphing Techniques
Completing the Square
The Vertex Formula
Quadratic Models and Curve Fitting
3.2 Synthetic Division	313	(7)
Synthetic Division
Evaluating Polynomial Functions Using the Remainder Theorem
Testing Potential Zeros
3.3 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
3.4 Polynomial Functions: Graphs, Applications, and Models	331	(18)
Graphs of f(x) = ax°
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)
3.5 Rational Functions: Graphs, Applications, and Models	350	(19)
The Reciprocal Function f(x) = 1/x
The Function f(x)= 1/x²
Asymptotes
Steps for Graphing Rational Functions
Rational Function Models
3.6 Variation	369	(8)
Direct Variation
Inverse Variation
Combined and Joint Variation
Summary	377	(4)
Review Exercises	381	(5)
Test	386	(2)
Quantitative Reasoning	388	(1)
4 Exponential and Logarithmic Functions	389	(84)
4.1 Inverse Functions	390	(12)
Inverse Operations
One-to-One Functions
Inverse Functions
Equations of Inverses
An Application of Inverse Functions to Cryptography
4.2 Exponential Functions	402	(16)
Exponents and Properties
Exponential Functions
Exponential Equations
Compound Interest
The Number e and Continuous Compounding
Exponential Models and Curve Fitting
4.3 Logarithmic Functions	418	(13)
Logarithms
Logarithmic Equations
Logarithmic Functions
Properties of Logarithms
Summary Exercises on Inverse, Exponential, and Logarithmic Functions	431	(1)
4.4 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
4.5 Exponential and Logarithmic Equations	443	(9)
Exponential Equations
Logarithmic Equations
Applications and Modeling
4.6 Applications and Models of Exponential Growth and Decay	452	(12)
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)
5 Systems and Matrices	473	(108)
5.1 Systems of Linear Equations	474	(17)
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
5.2 Matrix Solution of Linear Systems	491	(12)
The Gauss-Jordan Method
Special Systems
5.3 Determinant Solution of Linear Systems	503	(11)
Determinants
Cofactors
Evaluating n X n Determinants
Cramer's Rule
5.4 Partial Fractions	514	(6)
Decomposition of Rational Expressions
Distinct Linear Factors
Repeated Linear Factors
Distinct Linear and Quadratic Factors
Repeated Quadratic Factors
5.5 Nonlinear Systems of Equations	520	(11)
Solving Nonlinear Systems with Real Solutions
Solving Nonlinear Systems with Nonreal Complex Solutions
Applying Nonlinear Systems
Summary Exercises on Systems of Equations	531	(1)
5.6 Systems of Inequalities and Linear Programming	532	(11)
Solving Linear Inequalities
Solving Systems of Inequalities
Linear Programming
5.7 Properties of Matrices	543	(14)
Basic Definitions
Adding Matrices
Special Matrices
Subtracting Matrices
Multiplying Matrices
Applying Matrix Algebra
5.8 Matrix Inverses	557	(12)
Identity Matrices
Multiplicative Inverses
Solving Systems Using Inverse Matrices
Summary	569	(5)
Review Exercises	574	(4)
Test	578	(2)
Quantitative Reasoning	580	(1)
6 Analytic Geometry	581	(45)
6.1 Parabolas	582	(10)
Conic Sections
Horizontal Parabolas
Geometric Definition and Equations of Parabolas
An Application of Parabolas
6.2 Ellipses	592	(11)
Equations and Graphs of Ellipses
Translated Ellipses
Eccentricity
Applications of Ellipses
6.3 Hyperbolas	603	(8)
Equations and Graphs of Hyperbolas
Translated Hyperbolas
Eccentricity
6.4 Summary of the Conic Sections	611	(7)
Characteristics
Identifying Conic Sections
Geometric Definition of Conic Sections
Summary	618	(2)
Review Exercises	620	(2)
Test	622	(2)
Quantitative Reasoning	624	(2)
7 Further Topics in Algebra
7.1 Sequences and Series	626	(11)
Sequences
Series and Summation Notation
7.2 Arithmetic Sequences and Series	637	(9)
Arithmetic Sequences
Arithmetic Series
7.3 Geometric Sequences and Series	646	(11)
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Summary Exercises on Sequences and Series	657	(1)
7.4 The Binomial Theorem	658	(8)
A Binomial Expansion Pattern
Pascal's Triangle
n-Factorial
Binomial Coefficients
The Binomial Theorem
kth Term of a Binomial Expansion
7.5 Mathematical Induction	666	(6)
Proof by Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Proof of the Binomial Theorem
7.6 Counting Theory	672	(11)
Fundamental Principle of Counting
Permutations
Combinations
Distinguishing Between Permutations and Combinations
7.7 Basics of Probability	683	(11)
Basic Concepts
Complements and Venn Diagrams
Odds
Union of Two Events
Binomial Probability
Summary	694	(4)
Review Exercises	698	(3)
Test	701	(1)
Quantitative Reasoning	702	(1)
Appendix Sets	703	(6)
Glossary	709
Solutions to Selected Exercises S-1
Answers to Selected Exercises A-I
Index of Applications I-1
Index I-5