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

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`    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, andodd-numbered Problems in the Chapter Review:Putting It All Together. (All solutions aregrouped by chapter.)Index                                              691`