Modeling, Functions, and Graphs : Algebra for College Students (4TH)

Modeling, Functions, and Graphs : Algebra for College Students (4TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 819 p.
  • 言語 ENG,ENG
  • 商品コード 9780495113065
  • DDC分類 512

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 44 (12)
Inequalities
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)
Investigation 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)
Chapter 2 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 271(1)
Equations
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 amin 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)
Chapter 3 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 331(9)
Growth
Exponential Functions 340(15)
Graphs of Exponential Functions 340(2)
Transformations of Exponential Functions 342(1)
Comparing Exponential and Power 343(1)
Functions
Exponential Equations 344(2)
Graphical Solution of Exponential 346(9)
Equations
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 376(2)
Two Points
Doubling Time 378(3)
Half-Life 381(1)
Annuities and Amortization 382(9)
Chapter 4 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 403(1)
Function
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 409(1)
Function
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 435(2)
Continuously
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)
Chapter 5 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 491(2)
Completing the Square
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 515(1)
Tickets
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 531(7)
Algebraically
Curve Fitting 538(23)
Finding a Quadratic Function through 539(3)
Three Points
Finding an Equation in Vertex Form 542(10)
Chapter 6 Summary and Review 552(6)
Projects for Chapter 6 558(3)
Polynomial and Rational Functions 561(76)
Investigation 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 618(1)
Algebraically
Solving Equations with Fractions 619(1)
Graphically
Extraneous Solutions 619(2)
Formulas 621(6)
Chapter 7 Summary and Review 627(6)
Projects for Chapter 7 633(4)
Linear Systems 637(70)
Investigation 13 Interpolating 638(1)
Polynomials
Systems of Linear Equations in Two 639(15)
Variables
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 654(12)
Variables
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 667(1)
of a System
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)
Chapter 8 Summary and Review 700(5)
Projects for Chapter 8 705(2)
APPENDIX A Algebra Skills Refresher 707(90)
A.1 Numbers and Operations 707(6)
Order of Operations 707(1)
Parentheses and Fraction Bars 707(1)
Radicals 708(1)
Scientific Notation 709(4)
A.2 Linear Equations and Inequalities 713(7)
Solving Linear Equations 713(2)
Formulas 715(1)
Linear Inequalities 716(1)
Interval Notation 717(3)
A.3 Algebraic Expressions and Problem 720(9)
Solving
Problem Solving 722(1)
Supply and Demand 722(1)
Percent Problems 723(1)
Weighted Averages 724(5)
A.4 Graphs and Equations 729(7)
Reading a Graph 729(1)
Graphs of Equations 730(6)
A.5 Linear Systems in Two Variables 736(7)
Solving Systems by Substitution 736(1)
Solving Systems by Elimination 737(6)
A.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)
A.7 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)
A.8 Factoring Quadratic Trinomials 756(5)
Special Products and Factors 758(3)
A.9 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)
A.10 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 √a 777(1)
Extraneous Solutions to Radical 778(1)
Equations
Equations with More than One Radical 779(3)
A.11 Facts from Geometry 782(10)
Right Triangles and the Pythagorean 782(1)
Theorem
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)
A.12 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)
B.1 Getting Started 797(1)
A. On and Off 797(1)
B. Numbers and Operations 797(1)
C. Clear and Delete 798(1)
B.2 Entering Expressions 798(3)
A. Parentheses 798(1)
B. Exponents and Powers 799(1)
C. Roots 799(1)
D. Absolute Value 800(1)
E. Scientific Notation 801(1)
B.3 Editing Expressions 801(1)
A. Overwriting 801(1)
B. Recalling an Entry 801(1)
C. Inserting a Character 802(1)
D. Recalling an Answer 802(1)
B.4 Graphing an Equation 802(3)
A. Standard Window 802(1)
B. Tracing 803(1)
C. Multiple Graphs 803(1)
D. Setting the Window 803(1)
E. Intersect Feature 804(1)
F. Other Windows 804(1)
B.5 Making a Table 805(1)
A. Using the Auto Option 805(1)
B. Using the Ask Option 805(1)
B.6 Regression 806(1)
A. Making a Scatterplot 806(1)
B. Finding a Regression Equation 806(1)
C. Graphing the Regression Equation 807(1)
B.7 Function Notation and Transformations 807(2)
of Graphs
A. Function Notation 807(1)
B. Transformation of Graphs 808(1)
Glossary 809(10)
Bibliography 819
Answers to Odd-Numbered Problems 1 (1)
Index 1