9780321227577

College Algebra

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  • ISBN13:

    9780321227577

  • ISBN10:

    0321227573

  • Edition: 9th
  • Format: Hardcover
  • Copyright: 2009-01-01
  • Publisher: Addison Wesley
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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

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