# College Algebra

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## 0321227573

• Edition: 9th
• Format: Hardcover
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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.

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
 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
 Complex Fractions
 R.6 Rational Exponents
55(10)
 Negative Exponents and the Quotient Rule
 Rational Exponents
 Complex Fractions Revisited
65(11)
 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
 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
115(10)
 Completing the Square
 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
 1.6 Other Types of Equations
136(10)
 Rational Equations
 Summary Exercises on Solving Equations
146(1)
 1.7 Inequalities
146(14)
 Linear Inequalities
 Three-Part 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)
294(19)
 Graphing Techniques
 Completing the Square
 The Vertex Formula
 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
 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
 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