大学代数(第4版)<br>Explorations in College Algebra (4TH)

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大学代数(第4版)
Explorations in College Algebra (4TH)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 700 p.
  • 言語 ENG
  • 商品コード 9780471916888
  • DDC分類 512

Table of Contents

    Making Sense of Data and Functions
Describing Single-Variable Data 2 (11)
Visualizing Single-Variable Data 2 (4)
Mean and Median: What is ``Average'' 6 (1)
Anyway?
An Introduction to Algebra Aerobics 7 (6)
Describing Relationships between Two 13 (9)
Variables
Visualizing Two-Variable Data 13 (1)
Constructing a ``60-Second Summary'' 14 (2)
Using Equations to Describe Change 16 (6)
An Introduction to Functions 22 (7)
What is a Function? 22 (1)
Representing Functions in Multiple Ways 23 (1)
Independent and Dependent Variables 24 (1)
When is a Relationship Not a Function? 24 (5)
The Language of Functions 29 (10)
Function Notation 29 (4)
Domain and Range 33 (6)
Visualizing Functions 39 (10)
Is There a Maximum or Minimum Value? 39 (1)
Is the Function Increasing or 40 (1)
Decreasing?
Is the Graph Concave Up or Concave Down? 40 (2)
Getting the Big Idea 42 (7)
Chapter Summary 49 (1)
Check Your Understanding 50 (2)
Chapter 1 Review: Putting It All Together 52 (14)
Exploration 1.1 Collecting, 58 (3)
Representing, and Analyzing Data
Exploration 1.2 Picturing Functions 61 (2)
Exploration 1.3 Deducing Formulas to 63 (3)
Describe Data
Rates of Change and Linear Functions
Average Rates of Change 66 (5)
Describing Change in the U.S. 66 (1)
Population over Time
Defining the Average Rate of Change 67 (1)
Limitations of the Average Rate of 68 (3)
Change
Change in the Average Rate of Change 71 (5)
The Average Rate of Change is a Slope 76 (6)
Calculating Slopes 76 (6)
Putting a Slant on Data 82 (5)
Slanting the Slope: Choosing Different 82 (1)
End Points
Slanting the Data with Words and Graphs 83 (4)
Linear Functions: When Rates of Change 87 (7)
Are Constant
What If the U.S. Population Had Grown 87 (1)
at a Constant Rate?
Real Examples of a Constant Rate of 87 (3)
Change
The General Equation for a Linear 90 (4)
Function
Visualizing Linear Functions 94 (5)
The Effect of b 94 (1)
The Effect of m 94 (5)
Finding Graphs and Equations of Linear 99 (9)
Functions
Finding the Graph 99 (1)
Finding the Equation 100(8)
Special Cases 108(14)
Direct Proportionality 108(2)
Horizontal and Vertical Lines 110(2)
Parallel and Perpendicular Lines 112(2)
Piecewise Linear Functions 114(1)
The absolute value function 115(2)
Step functions 117(5)
Constructing Linear Models for Data 122(9)
Fitting a Line to Data: The Kalama Study 123(2)
Reinitializing the Independent Variable 125(1)
Interpolation and Extrapolation: Making 126(5)
Predictions
Chapter Summary 131(1)
Check Your Understanding 132(2)
Chapter 2 Review: Putting It All Together 134(12)
Exploration 2.1 Having It Your Way 139(2)
Exploration 2.2A Looking at Lines with 141(1)
the Course Software
Exploration 2.2B Looking at Lines with 142(4)
a Graphing Calculator
AN EXTENDED EXPLORATION: LOOKING FOR LINKS
BETWEEN EDUCATION AND EARNINGS
Using U.S. Census Data 146(2)
Summarizing the Data: Regression Lines 148(5)
Is There a Relationship between 148(3)
Education and Earnings?
Regression Lines: How Good a Fit? 151(2)
Interpreting Regression Lines: 153(1)
Correlation vs. Causation
Raising More Questions 154(3)
Do Earnings Depend on Age? 155(1)
Do Earnings Depend upon Gender? 155(2)
How Good are the Data? 157(1)
How Good is the Analysis? 157(1)
Exploring on Your Own 157(2)
Exercises 159(7)
When Lines Meet: Linear Systems
Systems of Linear Equations 166(5)
An Economic Comparison of Solar vs. 166(5)
Conventional Heating Systems
Finding Solutions to Systems of Linear 171(12)
Equations
Visualizing Solutions 171(1)
Strategies for Finding Solutions 172(4)
Linear Systems in Economics: Supply and 176(7)
Demand
Reading between the Lines: Linear 183(10)
Inequalities
Above and Below the Line 183(1)
Manipulating Inequalities 184(1)
Reading between the Lines 185(2)
Breakeven Points: Regions of Profit or 187(6)
Loss
Systems with Piecewise Linear Functions: 193(8)
Tax Plans
Graduated vs. Flat Income Tax 193(2)
Comparing the Two Tax Models 195(1)
The Case of Massachusetts 196(5)
Chapter Summary 201(1)
Check Your Understanding 202(2)
Chapter 3 Review: Putting It All Together 204(8)
Exploration 3.1 Flat vs. Graduated 209(3)
Income Tax: Who Benefits?
The Laws of Exponents and Logarithms:
Measuring the Universe
The Numbers of Science: Measuring Time 212(6)
and Space
Powers of 10 and the Metric System 212(2)
Scientific notation 214(4)
Positive Integer Exponents 218(8)
Exponent Rules 219(2)
Common Errors 221(2)
Estimating Answers 223(3)
Negative Integer Exponents 226(4)
Evaluating (a/b)--n 227(3)
Converting Units 230(5)
Converting Units within the Metric 230(1)
System
Converting between the Metric and 231(1)
English Systems
Using Multiple Conversion Factors 231(4)
Fractional Exponents 235(7)
Square Roots: Expressions of the Form 235(2)
a1/2
nth Roots: Expressions of the Form a1/n 237(1)
Rules for Radicals 238(1)
Fractional Powers: Expressions of the 239(3)
Form am/n
Orders of Magnitude 242(6)
Comparing Numbers of Widely Differing 242(1)
Sizes
Orders of Magnitude 242(2)
Graphing Numbers of Widely Differing 244(4)
Sizes: Log Scales
Logarithms Base 10 248(7)
Finding the Logarithms of Powers of 10 248(2)
Finding the Logarithm of Any Positive 250(1)
Number
Plotting Numbers on a Logarithmic Scale 251(4)
Chapter Summary 255(1)
Check Your Understanding 256(1)
Chapter 4 Review: Putting It All Together 257(9)
Exploration 4.1 The Scale and the Tale 260(2)
of the Universe
Exploration 4.2 Patterns in the 262(4)
Positions and Motions of the Planets
Growth and Decay: An Introduction to
Exponential Functions
Exponential Growth 266(5)
The Growth of E. coli Bacteria 266(1)
The General Exponential Growth Function 267(1)
Looking at Real Growth Data for E. coli 268(3)
Bacteria
Linear vs. Exponential Growth Functions 271(8)
Linear vs. Exponential Growth 271(2)
Comparing the Average Rates of Change 273(1)
A Linear vs. an Exponential Model 274(1)
through Two Points
Identifying Linear vs. Exponential 275(4)
Functions in a Data Table
Exponential Decay 279(5)
The Decay of Iodine-131 279(1)
The General Exponential Decay Function 279(5)
Visualizing Exponential Functions 284(6)
The Effect of the Base a 284(1)
The Effect of the Initial Value C 285(2)
Horizontal Asymptotes 287(3)
Exponential Functions: A Constant Percent 290(8)
Change
Exponential Growth: Increasing by a 290(1)
Constant Percent
Exponential Decay: Decreasing by a 291(2)
Constant Percent
Revisiting Linear vs. Exponential 293(5)
Functions
Examples of Exponential Growth and Decay 298(18)
Half-Life and Doubling Time 299(2)
The ``rule of 70'' 301(3)
Compound Interest Rates 304(4)
The Malthusian Dilemma 308(1)
Forming a Fractal Tree 309(7)
Semi-log Plots of Exponential Functions 316(4)
Chapter Summary 320(1)
Check Your Understanding 321(1)
Chapter 5 Review: Putting It All Together 322(8)
Exploration 5.1 Properties of 327(3)
Exponential Functions
Logarithmic Links: Logarithmic and
Exponential Functions
Using Logarithms to Solve Exponential 330(10)
Equations
Estimating Solutions to Exponential 330(1)
Equations
Rules for Logarithms 331(5)
Solving Exponential Equations 336(4)
Base e and Continuous Compounding 340(9)
What is e? 340(1)
Continuous Compounding 341(3)
Exponential Functions Base e 344(5)
The Natural Logarithm 349(3)
Logarithmic Functions 352(11)
The Graphs of Logarithmic Functions 353(1)
The Relationship between Logarithmic 354(1)
and Exponential Functions
Logarithmic vs. exponential growth 354(1)
Logarithmic and exponential functions 355(2)
are inverses of each other
Applications of Logarithmic Functions 357(1)
Measuring acidity: The pH scale 357(2)
Measuring noise: The decibel scale 359(4)
Transforming Exponential Functions to 363(6)
Base e
Converting a to ek 364(5)
Using Semi-log Plots to Construct 369(5)
Exponential Models for Data
Why Do Semi-Log Plots of Exponential 369(5)
Functions Produce Straight Lines?
Chapter Summary 374(1)
Check Your Understanding 375(2)
Chapter 6 Review: Putting It All Together 377(7)
Exploration 6.1 Properties of 380(4)
Logarithmic Functions
Power Functions
The Tension between Surface Area and 384(5)
Volume
Scaling Up a Cube 384(2)
Size and Shape 386(3)
Direct Proportionality: Power Functions 389(8)
with Positive Powers
Direct Proportionality 390(1)
Properties of Direct Proportionality 390(3)
Direct Proportionality with More Than 393(4)
One Variable
Visualizing Positive Integer Powers 397(8)
The Graphs of f(x) = x2 and g(x) = x3 397(2)
Odd vs. Even Powers 399(1)
Symmetry 400(1)
The Effect of the Coefficient k 400(5)
Comparing Power and Exponential Functions 405(4)
Which Eventually Grows Faster, a Power 405(4)
Function or an Exponential Function?
Inverse Proportionality: Power Functions 409(11)
with Negative Integer Powers
Inverse Proportionality 410(1)
Properties of Inverse Proportionality 411(4)
Inverse Square Laws 415(5)
Visualizing Negative Integer Power 420(9)
Functions
The Graphs of f(x) = x-1 and g(x) = x-2 420(2)
Odd vs. Even Powers 422(1)
Asymptotes 423(1)
Symmetry 423(1)
The Effect of the Coefficient k 423(6)
Using Logarithmic Scales to Find the Best 429(13)
Functional Model
Looking for Lines 429(1)
Why is a Log-Log Plot of a Power 430(1)
Function a Straight Line?
Translating Power Functions into 430(1)
Equivalent Logarithmic Functions
Analyzing Weight and Height Data 431(1)
Using a standard plot 431(1)
Using a semi-log plot 431(1)
Using a log-log plot 432(2)
Allometry: The Effect of Scale 434(8)
Chapter Summary 442(1)
Check Your Understanding 443(1)
Chapter 7 Review: Putting It All Together 444(10)
Exploration 7.1 Scaling Objects 448(2)
Exploration 7.2 Predicting Properties 450(1)
of Power Functions
Exploration 7.3 Visualizing Power 451(3)
Functions with Negative Integer Powers
Quadratics, Polynomials, and Beyond
An Introduction to Quadratic Functions 454(9)
The Simplest Quadratic 454(1)
Designing parabolic devices 455(1)
The General Quadratic 456(1)
Properties of Quadratic Functions 457(2)
Estimating the Vertex and Horizontal 459(4)
Intercepts
Finding the Vertex: Transformations of y 463(17)
= x2
Stretching and Compressing Vertically 464(1)
Reflections across the Horizontal Axis 464(1)
Shifting Vertically and Horizontally 465(3)
Using Transformations to Get the Vertex 468(2)
Form
Finding the Vertex from the Standard 470(2)
Form
Converting between Standard and Vertex 472(8)
Forms
Finding the Horizontal Intercepts 480(13)
Using Factoring to Find the Horizontal 481(1)
Intercepts
Factoring Quadratics 482(2)
Using the Quadratic Formula to Find the 484(1)
Horizontal Intercepts
The discriminant 485(2)
Imaginary and complex numbers 487(1)
The Factored Form 488(5)
The Average Rate of Change of a Quadratic 493(5)
Function
An Introduction to Polynomial Functions 498(12)
Defining a Polynomial Function 498(2)
Visualizing Polynomial Functions 500(2)
Finding the Vertical Intercept 502(1)
Finding the Horizontal Intercepts 503(7)
New Functions from Old 510(11)
Transforming a Function 510(1)
Stretching, compressing and shifting 510(1)
Reflections 511(1)
Symmetry 512(9)
Combining Two Functions 521(10)
The Algebra of Functions 521(3)
Rational Functions: The Quotient of Two 524(1)
Polynomials
Visualizing Rational Functions 525(6)
Composition and Inverse Functions 531(16)
Composing Two Functions 531(2)
Composing More Than Two Functions 533(1)
Inverse Functions: Returning the 534(6)
Original Value
A Final Example 540(7)
Chapter Summary 547(1)
Check Your Understanding 548(2)
Chapter 8 Review: Putting It All Together 550(10)
Exploration 8.1 How Fast Are You? Using 555(5)
a Ruler to Make a Reaction Timer
AN EXTENDED EXPLORATION: THE MATHEMATICS OF
MOTION
The Scientific Method 560(1)
The Free-Fall Experiment 560(10)
Interpreting Data from a Free-Fall 561(2)
Experiment
Deriving an Equation Relating Distance 563(2)
and Time
Returning to Galileo's Question 565(1)
Velocity: Change in Distance over Time 565(1)
Acceleration: Change in Velocity over 566(2)
Time
Deriving an Equation for the Height of 568(1)
an Object in Free Fall
Working with an Initial Upward Velocity 569(1)
Collecting and Analyzing Data from a Free 570(3)
Fall Experiment
Exercises 573(6)
Appendix Student Data Tables for Exploration 2.1 579(4)
Solutions For Algebra Aerobics, odd-numbered 583(108)
Exercises, Check Your Understanding, and
odd-numbered Problems in the Chapter Review:
Putting It All Together. (All solutions are
grouped by chapter.)
Index 691