cover -- copyright page -- title page -- Contents -- Preface -- To the Student -- To the Instructor -- Philosophy of the Book -- The Intended Audiences -- Suggested Courses Based on the Book -- Acknowledgments -- 1 Data Everywhere -- 1.1 Data in the Real World -- Measuring the Center of a Set of Data -- Measuring the Spread in a Set of Data -- How the Standard Deviation Formula Arises -- Quartiles -- Problems -- 1.2 Displaying Data -- Normally Distributed Data -- Box-and-Whisker Plots -- Problems -- 1.3 Two-Variable Data -- Simple Patterns in Data -- Problems -- Virtual Laboratory 1 -- 2 Functions Everywhere -- 2.1 Functions in the Real World -- Representing Functions with Formulas and Equations -- Representing Functions with Graphs -- Representing Functions with Tables -- Representing Functions with Words -- Why Study Functions? -- Connecting Between the Different Representations -- Problems -- 2.2 Describing the Behavior of Functions -- Increasing and Decreasing Functions -- Concavity: How A Function Bends -- Periodic Behavior -- Problems -- 2.3 Representing Functions Symbolically -- Domain and Range of a Function -- Proportionality -- Problems -- 2.4 Mathematical Models -- Parameters and Mathematical Models -- Problems -- 3 Linear Functions -- 3.1 Fundamental Concepts of Linear Functions -- Linear Functions That Pass Through the Origin -- The Graph of a Linear Function That Passes Through the Origin -- Lines That Don't Pass Through the Origin -- The Point-Slope Formula -- Problems -- Exercising Your Algebra Skills -- 3.2 Modeling With Linear Functions -- Problems -- 3.3 Linear Functions and Data -- Determining Whether a Set of Data Is Linear -- Capturing a Linear Pattern in Data -- z-Values -- Problems -- Exercising Your Algebra Skills -- 3.4 Linear Regression: Finding the Best Line -- The Least Squares Criterion.

Additional Examples of Linear Regression -- The Correlation Coefficient -- Variation among Samples -- Problems -- Virtual Laboratory 3.1: Biology -- Bradford Analysis for Protein Concentrations -- Virtual Laboratory 3.2: Physics -- Hooke's Law on the Elongation of a Spring -- 4 More about Linear Functions -- 4.1 Systems of Linear Equations -- Solving Systems of Linear Equations Geometrically -- Solving Systems of Linear Equations Algebraically -- Solving Systems of Linear Equations Using Matrices -- Problems -- 4.2 Applications of Linear Equations -- Solving the Regression Equations -- Balancing Chemical Equations -- Not Every System of Equations has a Solution -- Some Systems of Equations have Multiple Solutions -- Problems -- 4.3 Matrix Products and their Applications -- Two Competing Populations -- Comparing Successive Vectors -- How the Product of a Matrix and a Vector is Defined -- How the Product of Two Matrices is Defined -- What is the Inverse Matrix? -- Problems -- 4.4 Linear Models with Several Variables -- The Multiple Correlation Coefficient -- Performing Multivariate Regression in Excel -- Problems -- 5 Families of Nonlinear Functions -- 5.1 Exponential Growth Functions -- Comparing Linear and Exponential Growth -- Applications of Exponential Growth -- Doubling Time -- Predicting with Exponential Growth Functions -- Finding an Exponential Function Through Two Points -- Rules for Exponents -- Problems -- Exercising Your Algebra Skills -- 5.2 Exponential Decay Functions -- Half-life -- Radioactive Decay -- DeterminingWhether a Set of Data Is Exponential -- Comparing Linear and Exponential Functions -- Problems -- Exercising Your Algebra Skills -- 5.3 Fitting Exponential Functions to Data -- The Base e -- Problems -- 5.4 Logarithmic Functions -- How the Exponential Regression Function is Calculated.

Exponential Regression and the Correlation Coefficient -- Comparing Exponential and Logarithmic Functions -- Problems -- Exercising Your Algebra Skills -- 5.5 Modeling with Logarithmic Functions -- pH Values -- Intensity of Earthquakes and the Richter Scale -- Measuring the Intensity of Sounds -- Changing Bases -- Fitting Logarithmic Functions to Data -- How the Logarithmic Regression Function is Calculated -- Problems -- 5.6 Power Functions -- Behavior of Power Functions for x > 0 -- Behavior of Power Functions for x > 1 -- Applications of Power Functions -- The Power Function Through Two Points -- Problems -- Exercising Your Algebra Skills -- 5.7 Fitting Power Functions to Data -- How the Power Regression Equation is Calculated -- Some Applications -- Potential Problems when Fitting Power Functions to Data -- Problems -- 5.8 How Good Is the Fit? -- Interpreting the Graphs -- Interpreting the Correlation Coefficient -- Interpreting the Sum of the Squares -- may have measurements on the growth of bacteria in a test tube that might suggest exponential growth,but you know that such growth cannot continue indefinitely, so an exponential function will model thepopulation only for a short while.Other Measures -- Problems -- Virtual Laboratory 5.1: Kepler's Third Law of Planetary Motion -- Virtual Laboratory 5.2: Running Speed and Length of the Body -- 6 Polynomial Functions -- 6.1 Introduction to Polynomial Functions -- Polynomials of Degree 1: Linear Functions -- Polynomials of Degree 2: Quadratic Functions -- Polynomials of Degree 3: Cubic Functions -- Polynomials of Degree 4: Quartic Functions -- The Zeros of a Polynomial and the Roots of An Equation -- Problems -- Exercising Your Algebra Skills -- 6.2 The Behavior of Polynomial Functions -- Quadratic Polynomials -- Cubic Polynomials -- Polynomials of Degree n -- The End Behavior of a Polynomial.

Problems -- Exercising Your Algebra Skills -- 6.3 Modeling with Polynomial Functions -- The Path of a Projectile -- Fitting Polynomials to Data -- Deriving the Regression Equations -- Problems -- Virtual Laboratory 6.1: Biosciences and Social Sciences -- Virtual Laboratory 6.2: Physics -- 7 Extended Families of Functions -- 7.1 Building New Functions from Old: Shifting, Stretching, and Shrinking -- Shifting Functions -- Stretching and Shrinking Functions -- Problems -- Exercising Your Algebra Skills -- 7.2 Using Shifting and Stretching With Data -- Analyzing a Cooling Experiment -- Terminal Velocity in Skydiving -- Repeated Dosages of a Medication -- Using Shifts -- Using Stretches -- Modeling Normal Distributions -- Problems -- 7.3 The Central Limit Theorem and Confidence Intervals -- The Distribution of Sample Means -- Samples from the Normal Population -- Samples from the U-Shaped Population -- Estimating the Mean of a Population -- Exploring Confidence Intervals -- Problems -- 7.4 Functions of Several Variables: Tables, Contours, Formulas -- Functions of Several Variables via Tables -- Functions of Several Variables via Graphs -- Functions of Several Variables via Formulas -- Problems -- Virtual Laboratory 7: Chemistry -- 8 Modeling Periodic Phenomena -- 8.1 The Sinusoidal Functions Sine and Cosine -- The Sine Function -- The Cosine Function -- Problems -- 8.2 Modeling Periodic Behavior with the Sine and Cosine -- The Vertical Shift or Midline -- The Amplitude -- The Frequency and the Period -- Fitting Sinusoidal Functions to Data -- Problems -- 8.3 Solving Equations with Sine and Cosine -- Problems -- 8.4 Approximating the Sine and Cosine with Polynomials -- Approximating the Sine Function -- Using Linear Regression -- Improving on the Linear Approximation to the Sine -- Patterns in the Approximation Formulas.

Improving the Approximation Using the Behavior of sin x -- Approximating the Cosine Function -- Problems -- Virtual Laboratory 8: Meteorology -- Appendices -- Appendix A: Some Mathematical Momentsto Remember -- Appendix B: Statistical Calculations on TI Calculators -- Using the STAT Features of the TI-84 Family -- Using the STAT Features of the TI-89 -- Appendix C: Statistical Calculations In Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix D: The Algebra of Linear Functions -- The Distributive Law -- Converting between the slope-intercept form and the point-slope form of a line -- Predictions with linear functions based on values of the independent variable -- Predicting with linear functions based on values of the dependent variable-solving linear equations -- The normal form for the equation of a line -- Appendix E: Solving Equations Graphically: Zoom-and-Trace -- Appendix F: Linear Regression on TI Calculators -- Using the STAT Features of the TI-83/84 Family -- Using the STAT Features of the TI-89 -- Appendix G: Linear Regression Using Excel -- To Draw a Scatterplot of Data in Excel 2003 -- To Add the Regression Line or Curve to a Scatterplot -- To Draw a Scatterplot of Data in Excel 2007 -- To Add the Regression Line or Curve to a Scatterplot -- Appendix H: Where the Correlation Coefficient Formula Comes From -- Appendix I: Solving Systems of Linear Equations Algebraically -- Appendix J: Curve Fitting in Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix K: Symmetry -- Appendix L: The Arithmetic of Complex Numbers -- M World Population Data for 2009 -- Selected Short Answers -- Chapter 1 -- Section 1.1 -- Section 1.2 -- Section 1.3 -- Chapter 2 -- Section 2.1 -- Section 2.2 -- Section 2.3 -- Section 2.4 -- Chapter 3 -- Section 3.1 -- Section 3.2 -- Section 3.3 -- Section 3.4.

Chapter 4.