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College Algebra in Context : With Applications for the Managerial, Life, and Social Sciences

by ;
Edition:
2nd
ISBN13:

9780321369581

ISBN10:
0321369580
Format:
Hardcover
Pub. Date:
1/1/2007
Publisher(s):
Addison Wesley

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Summary

Learn the Skills. Apply the Concepts. This second EDITION of College Algebra in Context continues to be application driven, and uses real-data problems to motivate student interest in the skills and concepts of algebra. The focus on real-world applications is designed to correspond to problems that students may encounter when they move on to future math classes or when they enter the work force. This EDITION contains improved content and a greater focus on motivating students to succeed in the course through its emphasis on applications.

Table of Contents

Preface xiii
List of Supplements
xvii
To the Student xix
Functions, Graphs, and Models; Linear Functions
1(138)
Algebra Toolbox
2(8)
Sets
2(1)
The Real Numbers
3(1)
Inequalities and Intervals on the Number Line
4(1)
Absolute Value
5(1)
Algebraic Expressions
5(1)
Removing Parentheses
6(1)
Solving Equations
6(2)
The Coordinate System
8(1)
Subscripts
8(2)
Functions and Models
10(17)
Function Definitions
10(2)
Tests for Functions
12(2)
Functional Notation
14(2)
Mathematical Models
16(1)
Domains and Ranges
17(10)
Graphs of Functions
27(14)
Graphs of Functions
27(1)
Graphing with Technology
28(4)
Aligning Data
32(1)
Determining Viewing Windows
32(2)
Graphing Data Points
34(7)
Linear Functions
41(14)
Linear Functions
41(1)
Intercepts
42(3)
Slope of a Line
45(2)
Slope and y-Intercept of a Line
47(2)
Constant Rate of Change
49(1)
Parallel and Perpendicular Lines
50(5)
Equations of Lines
55(15)
Writing Equations of Lines
55(5)
Average Rate of Change
60(2)
Approximately Linear Data
62(8)
Algebraic and Graphical Solutions of Linear Equations
70(12)
Algebraic Solution of Linear Equations
71(2)
Solutions, Zeros, and x-lntercepts
73(1)
Graphical Solution of Linear Equations
74(3)
Formulas; Solving an Equation for a Specified Linear Variable
77(5)
Fitting Lines to Data Points; Modeling Linear Functions
82(20)
Fitting Lines to Data Points
82(3)
Linear Regression
85(3)
Modeling Discrete Data with Linear Functions
88(4)
Applying Models
92(1)
Goodness of Fit
92(10)
Systems of Linear Equations in Two Variables
102(12)
Graphical Solution of Systems
102(3)
Solution by Substitution
105(2)
Solution by Elimination
107(1)
Modeling Systems of Linear Equations
108(2)
Inconsistent and Dependent Systems
110(4)
Solutions of Linear Inequalities
114(25)
Algebraic Solution of Linear Inequalities
114(3)
Graphical Solution of Linear Inequalities
117(2)
x-lntercept Method
119(1)
Double Inequalities
120(6)
Summary
126(1)
Key Concepts and Formulas
126(5)
Skills Check
131(1)
Review
132(5)
Group Activities/Extended Applications
137(2)
Quadratic and Other Nonlinear Functions
139(136)
Algebra Toolbox
140(14)
Properties of Exponents
140(1)
Roots and Radicals
141(1)
Radicals and Rational Exponents
142(1)
Polynomials
143(1)
Multiplication of Polynomials
144(2)
Factoring
146(3)
Solving Literal Equations
149(1)
Imaginary and Complex Numbers
149(1)
Operations with Complex Numbers
150(4)
Quadratic Functions; Parabolas
154(11)
Parabolas
154(5)
Quadratic Functions in the Form f(x) = a(x - h)2 + k
159(1)
Intercepts
160(5)
Solving Quadratic Equations
165(16)
Factoring Methods
165(2)
Graphical Methods
167(1)
Combining Graphs and Factoring
168(2)
Graphical and Numerical Methods
170(1)
The Square Root Method
170(1)
Completing the Square
171(1)
The Quadratic Formula
172(2)
The Discriminant
174(1)
Aids for Solving Quadratic Equations
175(1)
Equations with Compiex Solutions
175(6)
A Library of Functions
181(12)
Power Functions
181(4)
Reciprocal Function
185(2)
Piecewise-Defined Functions
187(2)
Absolute Value Function
189(4)
Transformations of Graphs and Symmetry
193(15)
Shifts of Graphs of Functions
193(3)
Stretching and Compressing Graphs
196(1)
Reflections of Graphs
197(3)
Symmetry; Even and Odd Functions
200(8)
Quadratic and Power Models
208(17)
Modeling with Quadratic Functions
208(1)
Comparison of Linear and Quadratic Models
209(3)
Modeling with Power Functions
212(2)
Comparison of Power and Quadratic Models
214(11)
Combining Functions; Composite Functions
225(12)
Operations with Functions
225(1)
Revenue, Cost, and Profit
226(3)
CompSsition of Functions
229(8)
Inverse Functions
237(12)
Inverse Functions
237(6)
Inverse Functions on Limited Domains
243(6)
Additional Equations and Inequalities
249(26)
Radical Equations; Equations Involving Rational Powers
249(2)
Equations Containing Rational Powers
251(1)
Solving Absolute Value Equations
252(1)
Inequalities Involving Absolute Values
253(1)
Solution of Quadratic Inequalities
254(4)
Power Inequalities
258(3)
Summary
261(1)
Key Concepts and Formulas
262(4)
Skills Check
266(1)
Review
267(6)
Group Activities/Extended Applications
273(2)
Exponential and Logarithmic Functions
275(94)
Algebra Toolbox
276(5)
Zero and Negative Exponents
276(2)
Scientific Notation
278(1)
Simple Interest
279(2)
Exponential Functions
281(10)
Exponential Functions
281(1)
Transformations of Graphs of Exponential Functions
282(1)
Exponential Growth
283(2)
Exponential Decay
285(1)
The Number e
286(5)
Logarithmic Functions
291(12)
Logarithmic Functions
291(4)
Common Logarithms
295(2)
Natural Logarithms
297(2)
Solution of Logarithmic Equations
299(4)
Exponential and Logarithmic Equations; Properties of Logarithms
303(14)
Solving Exponential Equations Using Logarithmic Forms
303(2)
Logarithmic Properties
305(3)
Change of Base
308(2)
Solving Exponential Equations Using Logarithmic Properties
310(2)
Solution of Logarithmic Equations
312(1)
Exponential thequalities
313(4)
Exponential and Logarithmic Models
317(15)
Modeling with Exponential Functions
317(3)
Constant Percent Change in Exponential Models
320(2)
Exponential Models
322(1)
Comparison of Models
323(1)
Logarithmic Models
324(3)
Exponents, Logarithms, and Linear Regression
327(5)
Exponential Functions and Investing
332(9)
Compound Interest
332(2)
Continuous Compounding and the Number e
334(3)
Present Value of an Investment
337(1)
Investment Models
338(3)
Annuities; Loan Repayment
341(8)
Future Value of an Annuity
341(2)
Present Value of an Annuity
343(1)
Loan Repayment
344(5)
Logistic and Gompertz Functions
349(20)
Logistic Functions
349(5)
Gompertz Functions
354(5)
Summary
359(1)
Key Concepts and Formulas
359(3)
Skills Check
362(1)
Review
363(4)
Group Activities/Extended Applications
367(2)
Higher-Degree Polynomial and Rational Functions
369(76)
Algebra Toolbox
370(7)
Polynomiais
370(1)
Factoring Higher-Degree Polynomials
370(1)
Rational Expressions
371(1)
Multiplying and Dividing Rational Expressions
372(1)
Adding and Subtracting Rational Expressions
373(1)
Division of Polynomiais
374(3)
Higher-Degree Polynomial Functions
377(10)
Cubic Functions
378(3)
Quartic Functions
381(6)
Modeling Cubic and Quartic Functions
387(13)
Modeling with Cubic Functions
387(3)
Modeling with Quartic Functions
390(1)
Model Comparisons
391(1)
Third and Fourth Differences
392(8)
Solution of Polynomial Equations
400(10)
Solving Polynomial Equations by Factoring
400(3)
Solution Using Factoring by Grouping
403(1)
The Root Method
403(2)
Estimating Solutions with Technology
405(5)
Polynomial Equations Continued; Fundamental Theorem of Algebra
410(10)
Division of Polynomials; Synthetic Division
410(2)
Using Synthetic Division to Solve Cubic Equations
412(1)
Graphs and Solutions
412(2)
Rational Solutions Test
414(2)
Fundamental Theorem of Algebra
416(4)
Rational Functions and Rational Equations
420(11)
Graphs of Rational Functions
420(5)
Analytical and Graphical Solution of Rational Equations
425(6)
Polynomial and Rational Inequalities
431(14)
Polynomial Inequalities
431(2)
Rational Inequalities
433(4)
Summary
437(1)
Key Concepts and Formutas
437(3)
Skills Check
440(1)
Review
441(2)
Group Activities/Extended Applications
443(2)
Systems of Equations and Matrices
445(74)
Algebra Toolbox
446(4)
Proportion
446(1)
Proportional Triples
447(1)
Linear Equations in Three Variables
447(3)
Systems of Linear Equations in Three Variables
450(11)
Systems in Three Variables
450(1)
Left-to-Right Elimination
451(2)
Modeling Systems of Equations
453(1)
Nonunique Solutions
454(7)
Matrix Solution of Systems of Linear Equations
461(14)
Matrix Representation of Systems of Equations
461(1)
Echelon Forms of Matrices; Solving Systems with Matrices
462(2)
Gauss-Jordan Elimination
464(1)
Solution with Technology
465(1)
Nonunique Solution
466(1)
Dependent Systems
467(2)
Inconsistent Systems
469(6)
Matrix Operations
475(15)
Addition and Subtraction of Matrices
475(4)
Multiplication of a Matrix by a Number
479(1)
Matrix Multiplication
480(3)
Multiplication with Technology
483(7)
Inverse Matrices; Matrix Equations
490(14)
Inverse Matrices
490(2)
Inverses and Technology
492(1)
Encoding and Decoding Messages
493(3)
Matrix Equations
496(2)
Matrix Equations and Technology
498(6)
Systems of Nonlinear Equations
504(15)
Algebraic Solution of Nonlinear Systems
504(3)
Graphical Solution of Nonlinear Systems
507(4)
Summary
511(1)
Key Concepts and Formulas
511(2)
Skills Check
513(1)
Review
514(3)
Group Activities/Extended Applications
517(2)
Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus
519
Systems of Inequalities
520(12)
Linear Inequalities in Two Variables
520(2)
Systems of Inequalities in Two Variables
522(4)
Systems of Nonlinear inequalities
526(6)
Linear Programming: Graphical Methods
532(11)
Linear Programming
532(6)
Solution with Technology
538(5)
Sequences and Discrete Functions
543(9)
Sequences
543(2)
Arithmetic Sequences
545(2)
Geometric Sequences
547(5)
Series
552(8)
Finite and Infinite Series
552(1)
Arithmetic Series
553(2)
Geometric Series
555(2)
Infinite Geometric Series
557(3)
Preparing for Calculus
560
Skills
560(2)
Skills
562(3)
Skills
565(1)
Skills
566(4)
Summary
570(1)
Key Concepts and Formulas
570(2)
Skills Check
572(1)
Review
573(2)
Group Activity/Extended Application
575
Answers to Selected Exercises 1(1)
Index 1


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