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Modeling, Functions, and Graphs Algebra for College Students (with iLrn™ Printed Access Card),9780534419417
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Modeling, Functions, and Graphs Algebra for College Students (with iLrn™ Printed Access Card)

by ;
Edition:
4th
ISBN13:

9780534419417

ISBN10:
0534419410
Format:
Hardcover
Pub. Date:
8/25/2006
Publisher(s):
Cengage Learning
List Price: $278.95

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Summary

The Fourth Edition of Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data.

Table of Contents

Functions and Their Graphs
1(122)
Investigation 1 Sales on Commission
2(1)
Linear Models
3(16)
Tables, Graphs, and Equations
3(2)
Choosing Scales for the Axes
5(2)
Linear Equations
7(2)
Intercepts
9(1)
Intercept Method for Graphing Lines
10(9)
Functions
19(20)
Definition of Function
19(1)
Functions Defined by Tables
20(1)
Functions Defined by Graphs
21(2)
Functions Defined by Equations
23(1)
Function Notation
24(1)
Evaluating a Function
25(2)
Operations with Function Notation
27(12)
Graphs of Functions
39(17)
Reading Function Values from a Graph
39(2)
Constructing the Graph of a Function
41(1)
The Vertical Line Test
42(2)
Graphical Solution of Equations and Inequalities
44(12)
Slope and Rate of Change
56(21)
Using Ratios for Comparison
56(1)
Measuring Steepness
57(1)
Definition of Slope
58(1)
Notation for Slope
59(2)
Lines Have Constant Slope
61(1)
Meaning of Slope
62(1)
A Formula for Slope
63(14)
Linear Functions
77(15)
Slope-Intercept Form
77(2)
Slope-Intercept Method of Graphing
79(1)
Finding a Linear Equation from a Graph
80(1)
Point-Slope Form
81(11)
Linear Regression
92(31)
Fitting a Line through Two Points
92(1)
Scatterplots
93(2)
Linear Regression
95(2)
Linear Interpolation and Extrapolation
97(14)
Summary and Review
111(9)
Projects for Chapter 1
120(3)
Modeling with Functions
123(110)
Investigation 2 Epidemics
124(1)
Investigations 3 Perimeter and Area
125(1)
Nonlinear Models
126(13)
Solving Nonlinear Equations
126(2)
Solving Formulas
128(1)
More Extraction of Roots
128(1)
Compound Interest and Inflation
129(1)
Other Nonlinear Equations
130(9)
Some Basic Functions
139(15)
Absolute Value
139(2)
Examples of Models
141(1)
Investigation 4 Eight Basic Functions
142(2)
Graphs of Eight Basic Functions
144(1)
Properties of the Basic Functions
144(2)
Functions Defined Piecewise
146(8)
Transformations of Graphs
154(21)
Vertical Translations
154(2)
Horizontal Translations
156(3)
Scale Factors
159(16)
Functions as Mathematical Models
175(17)
The Shape of the Graph
175(3)
Using the Basic Functions as Models
178(2)
Modeling with Piecewise Functions
180(12)
The Absolute Value Function
192(11)
Absolute Value Equations
193(2)
Absolute Value Inequalities
195(1)
Using the Absolute Value in Modeling
196(2)
Measurement Error
198(5)
Domain and Range
203(30)
Definitions of Domain and Range
203(1)
Finding Domain and Range from a Graph
204(3)
Finding the Domain from a Formula
207(1)
Restricting the Domain
208(7)
Summary and Review
215(9)
Projects for Chapter 2
224(9)
Power Functions
233(88)
Investigation 5 Inflating a Balloon
234(1)
Variation
235(20)
Direct Variation
235(2)
The Scaling Property of Direct Variation
237(2)
Finding a Formula for Direct Variation
239(1)
Direct Variation with a Power of x
240(1)
Scaling
241(1)
Inverse Variation
242(2)
Finding a Formula for Inverse Variation
244(11)
Integer Exponents
255(13)
Negative Exponents
255(2)
Power Functions
257(3)
Working with Negative Exponents
260(1)
Laws of Exponents
260(8)
Roots and Radicals
268(14)
nth Roots
268(1)
Exponential Notation for Radicals
268(2)
Irrational Numbers
270(1)
Using Fractional Exponents to Solve Equations
271(1)
Power Functions
272(1)
Solving Radical Equations
273(2)
A Note on Roots of Negative Numbers
275(7)
Rational Exponents
282(15)
Powers of the Form am/n
282(1)
Power Functions
283(1)
More About Scaling
284(1)
Radical Notation
285(1)
Operations with Rational Exponents
286(1)
Solving Equations
287(1)
Investigation 6 Vampire Bats
287(10)
Joint Variation
297(24)
Functions of Two or More Variables
297(1)
Tables of Values
298(1)
Joint Variation
299(3)
Graphs
302(9)
Summary and Review
311(7)
Projects for Chapter 3
318(3)
Exponential Functions
321(80)
Investigation 7 Population Growth
322(1)
Exponential Growth and Decay
323(17)
Exponential Growth
323(1)
Growth Factors
324(1)
Percent Increase
325(3)
Exponential Decay
328(1)
Investigation 8 Exponential Decay
328(1)
Decay Factors
329(2)
Comparing Linear Growth and Exponential Growth
331(9)
Exponential Functions
340(15)
Graphs of Exponential Functions
340(2)
Transformations of Exponential Functions
342(1)
Comparing Exponential and Power Functions
343(1)
Exponential Equations
344(2)
Graphical Solution of Exponential Equations
346(9)
Logarithms
355(10)
Using the Conversion Equations
357(1)
Approximating Logarithms
357(2)
Base 10 Logarithms
359(1)
Solving Exponential Equations
359(2)
Application to Exponential Models
361(4)
Properties of Logarithms
365(11)
Using the Properties of Logarithms
366(1)
Solving Exponential Equations
367(2)
Applications
369(1)
Compound Interest
370(1)
Solving Formulas
371(5)
Exponential Models
376(25)
Fitting an Exponential Function through Two Points
376(2)
Doubling Time
378(3)
Half-Life
381(1)
Annuities and Amortization
382(9)
Summary and Review
391(6)
Projects for Chapter 4
397(4)
Logarithmic Functions
401(74)
Inverse Functions
402(19)
Finding a Formula for the Inverse Function
403(1)
Inverse Function Notation
404(2)
Graph of the Inverse Function
406(1)
When Is the Inverse a Function?
407(2)
Mathematical Properties of the Inverse Function
409(1)
Symmetry
410(2)
Domain and Range
412(9)
Logarithmic Functions
421(16)
Inverse of the Exponential Function
421(3)
Graphs of Logarithmic Functions
424(2)
Evaluating Logarithmic Functions
426(1)
Logarithmic Equations
426(2)
Using the Properties of Logarithms
428(7)
Investigation 9 Interest Compounded Continuously
435(2)
The Natural Base
437(14)
The Natural Exponential Function
437(1)
The Natural Logarithmic Function
438(1)
Properties of the Natural Logarithm
439(1)
Solving Equations
440(1)
Exponential Growth and Decay
441(2)
Continuous Compounding
443(8)
Logarithmic Scales
451(24)
Using Log Scales
453(1)
Equal Increments on a Log Scale
454(2)
Acidity and the pH Scale
456(2)
Decibels
458(1)
The Richter Scale
459(7)
Summary and Review
466(6)
Projects for Chapter 5
472(3)
Quadratic Functions
475(86)
Investigation 10 Height of a Baseball
476(1)
Factors and x-Intercepts
477(12)
Zero-Factor Principle
477(1)
Solving Quadratic Equations by Factoring
478(3)
Applications
481(1)
Solutions of Quadratic Equations
481(1)
Equations Quadratic in Form
482(7)
Solving Quadratic Equations
489(12)
Squares of Binomials
489(2)
Solving Quadratic Equations by Completing the Square
491(2)
The General Case
493(2)
Quadratic Formula
495(1)
Applications
496(5)
Graphing Parabolas
501(14)
The Graph of y = ax2
501(1)
The Graph of y = x2 + c
502(1)
The Graph of y = ax2 + bx
503(1)
Finding the Vertex
504(1)
The Graph of y = ax2 + bx + c
505(1)
Number of x-Intercepts
506(1)
Sketching a Parabola
507(8)
Problem Solving
515(13)
Investigation 11 Revenue from Theater Tickets
515(1)
Maximum or Minimum Values
516(1)
The Vertex Form for a Parabola
517(2)
Graphing with the Vertex Form
519(1)
Systems Involving Quadratic Equations
519(9)
Quadratic Inequalities
528(10)
Solving Inequalities Graphically
528(3)
Solving Quadratic Inequalities Algebraically
531(7)
Curve Fitting
538(23)
Finding a Quadratic Function through Three Points
539(3)
Finding an Equation in Vertex Form
542(10)
Summary and Review
552(6)
Projects for Chapter 6
558(3)
Polynomial and Rational Functions
561(76)
Investigations 12 Bezier Curves
562(3)
Polynomial Functions
565(12)
Products of Polynomials
566(1)
Special Products
567(1)
Factoring Cubics
568(1)
Modeling with Polynomials
569(8)
Graphing Polynomial Functions
577(11)
Classifying Polynomials by Degree
577(1)
Cubic Polynomials
578(1)
Quartic Polynomials
579(1)
x-Intercepts and the Factor Theorem
580(2)
Zeros of Multiplicity Two or Three
582(6)
Complex Numbers
588(12)
Imaginary Numbers
588(1)
Complex Numbers
589(1)
Arithmetic of Complex Numbers
590(1)
Products of Complex Numbers
591(1)
Quotients of Complex Numbers
592(1)
Zeros of Polynomials
593(2)
Graphing Complex Numbers
595(5)
Graphing Rational Functions
600(17)
Domain of a Rational Function
603(1)
Vertical Asymptotes
604(2)
Horizontal Asymptotes
606(2)
Applications
608(9)
Equations That Include Algebraic Fractions
617(20)
Solving Equations with Fractions Algebraically
618(1)
Solving Equations with Fractions Graphically
619(1)
Extraneous Solutions
619(2)
Formulas
621(6)
Summary and Review
627(6)
Projects for Chapter 7
633(4)
Linear Systems
637(70)
Investigation 13 Interpolating Polynomials
638(1)
Systems of Linear Equations in Two Variables
639(15)
Solving Systems by Graphing
639(4)
Inconsistent and Dependent Systems
643(3)
Applications
646(2)
An Application from Economics
648(6)
Systems of Linear Equations in Three Variables
654(12)
3 X 3 Linear Systems
654(2)
Back-Substitution
656(1)
Gaussian Reduction
657(3)
Inconsistent and Dependent Systems
660(1)
Applications
661(5)
Solving Linear Systems Using Matrices
666(16)
Coefficient Matrix and Augmented Matrix of a System
667(1)
Elementary Row Operations
667(3)
Matrix Reduction
670(1)
Reducing a 3 X 3 Matrix
671(2)
Solving Larger Systems
673(7)
Investigation 14 Input-Output Models
680(2)
Linear Inequalities
682(8)
Graphs of Inequalities in Two Variables
682(1)
Linear Inequalities
683(1)
Using a Test Point
684(2)
Systems of Inequalities
686(4)
Linear Programming
690(17)
The Objective Function and Constraints
690(1)
Feasible Solutions
691(1)
The Optimum Solution
692(8)
Summary and Review
700(5)
Projects for Chapter 8
705(2)
APPENDIX A Algebra Skills Refresher
707(90)
Numbers and Operations
707(6)
Order of Operations
707(1)
Parentheses and Fraction Bars
707(1)
Radicals
708(1)
Scientific Notation
709(4)
Linear Equations and Inequalities
713(7)
Solving Linear Equations
713(2)
Formulas
715(1)
Linear Inequalities
716(1)
Interval Notation
717(3)
Algebraic Expressions and Problem Solving
720(9)
Problem Solving
722(1)
Supply and Demand
722(1)
Percent Problems
723(1)
Weighted Averages
724(5)
Graphs and Equations
729(7)
Reading a Graph
729(1)
Graphs of Equations
730(6)
Linear Systems in Two Variables
736(7)
Solving Systems by Substitution
736(1)
Solving Systems by Elimination
737(6)
Laws of Exponents
743(6)
Product of Powers
743(1)
Quotients of Powers
744(1)
Power of a Power
745(1)
Power of a Product
746(1)
Power of a Quotient
746(3)
Polynomials and Factoring
749(7)
Polynomials
749(1)
Products of Polynomials
750(1)
Products of Binomials
751(1)
Factoring
751(1)
Common Factors
751(1)
Opposite of a Binomial
752(1)
Polynomial Division
752(4)
Factoring Quadratic Trinomials
756(5)
Special Products and Factors
758(3)
Working with Algebraic Fractions
761(12)
Reducing Fractions
761(2)
Products of Fractions
763(1)
Quotients of Fractions
764(1)
Sums and Differences of Like Fractions
764(1)
Lowest Common Denominator
765(1)
Building Fractions
766(1)
Sums and Differences of Unlike Fractions
766(2)
Complex Fractions
768(1)
Negative Exponents
769(4)
Working with Radicals
773(9)
Properties of Radicals
773(1)
Simplifying Radicals
773(2)
Sums and Differences of Radicals
775(1)
Products of Radicals
775(1)
Rationalizing the Denominator
776(1)
Simplifying n√an
777(1)
Extraneous Solutions to Radical Equations
778(1)
Equations with More than One Radical
779(3)
Facts from Geometry
782(10)
Right Triangles and the Pythagorean Theorem
782(1)
Isosceles and Equilateral Triangles
783(1)
The Triangle Inequality
783(1)
Similar Triangles
784(1)
Volume and Surface Area
785(1)
The Distance Formula
786(1)
The Midpoint Formula
787(1)
Circles
788(4)
The Real Number System
792(5)
Subsets of the Real Numbers
792(1)
Rational Numbers
793(1)
Irrational Numbers
793(1)
Properties of the Real Numbers
794(1)
Order Properties of the Real Numbers
795(2)
APPENDIX B Using a Graphing Calculator
797(12)
Getting Started
797(1)
On and Off
797(1)
Numbers and Operations
797(1)
Clear and Delete
798(1)
Entering Expressions
798(3)
Parentheses
798(1)
Exponents and Powers
799(1)
Roots
799(1)
Absolute Value
800(1)
Scientific Notation
801(1)
Editing Expressions
801(1)
Overwriting
801(1)
Recalling an Entry
801(1)
Inserting a Character
802(1)
Recalling an Answer
802(1)
Graphing an Equation
802(3)
Standard Window
802(1)
Tracing
803(1)
Multiple Graphs
803(1)
Setting the Window
803(1)
Intersect Feature
804(1)
Other Windows
804(1)
Making a Table
805(1)
Using the Auto Option
805(1)
Using the Ask Option
805(1)
Regression
806(1)
Making a Scatterplot
806(1)
Finding a Regression Equation
806(1)
Graphing the Regression Equation
807(1)
Function Notation and Transformations of Graphs
807(2)
Function Notation
807(1)
Transformation of Graphs
808(1)
Glossary 809(10)
Bibliography 819
Answers to Odd-Numbered Problems 1(1)
Index 1


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