# Essentials of College Algebra

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## 0321385233

• Edition: 1st
• Format: Paperback
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### 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.

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
 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
 Complex Fractions
 Rational Exponents
55(10)
 Negative Exponents and the Quotient Rule
 Rational Exponents
 Complex Fractions Revisited
65(20)
 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
 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
115(10)
 Completing the Square
 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
 Other Types of Equations
136(10)
 Rational Equations
 Summary Exercises on Solving Equations
146(1)
 Inequalities
146(14)
 Linear Inequalities
 Three-Part 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)
294(19)
 Graphing Techniques
 Completing the Square
 The Vertex Formula
 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)