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Essentials of College Algebra

ISBN: 9780321385239 | 0321385233
Edition: 1st
Format: Paperback
Publisher: Addison Wesley
Pub. Date: 1/1/2007

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SummaryTable of Contents
Focused on helping students develop both the conceptual understanding and the analytical skills necessary to experience success 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.
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Prefacevii
Supplements Guidexi
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 Sets533(6)
Glossary539
Solutions to Selected Exercises1(1)
Answers to Selected Exercises1(1)
Index of Applications1(4)
Index5

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