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An Introduction to Data and Functions | |
Describing Single-Variable Data | |
Visualizing Single-Variable Data | |
Numerical Descriptors: What is "Average" Anyway? | |
An Introduction to Algebra Aerobics | |
An Introduction to Explore and Extend | |
Describing Relationships between Two Variables | |
Visualizing Two-Variable Data | |
Constructing a "60-Second Summary" | |
Using Equations to Describe Change | |
An Introduction to Functions | |
What is a Function? | |
Representing Functions: Words, Tables, Graphs and Equations | |
Input and Output: Independent and Dependent Variables | |
When is a Relationship Not a Function? | |
The Language of Functions | |
Function Notation | |
Domain and Range | |
Visualizing Functions | |
Is There a Maximum or Minimum Value? | |
When is the Output of the Function Positive, Negative or Zero? | |
Is the Function Increasing or Decreasing? | |
Is the Graph Concave Up or Concave Down? | |
Getting the Big Idea | |
Chapter Summary | |
Check Your Understanding | |
Chapter 1 Review: Putting it all Together | |
Exploration 1.1 Collecting, Representing, and Analyzing Data | |
Rates of Change and Linear Function | |
Average Rates of Change | |
Describing Change in the U.S. Population over Time | |
Defining the Average Rate of Change | |
Limitations of the Average Rate of Change | |
Change in the Average Rate of Change | |
The Average Rate of Change is a Slope | |
Calculating Slopes | |
Putting a Slant on Data | |
Slanting the Slope: Choosing Different End Points | |
Slanting the Data with Words and Graphs | |
Linear Functions: When Rates of Change are Constant | |
What if the U.S. Population Had Grown at a Constant Rate? | |
Real Examples of a Constant Rate of Change | |
The General Equation for a Linear Function | |
Visualizing Linear Functions | |
The Effect of b | |
The Effect of m | |
Finding Graphs and Equations of Linear Functions | |
Finding the Graph | |
Finding the Equation | |
Special Cases | |
Direct Proportionality | |
Horizontal and Vertical Lines | |
Parallel and Perpendicular Lines | |
Breaking the Line: Piecewise Linear Functions | |
Piecewise Linear Functions | |
The absolute value function | |
Step functions | |
Constructing Linear Models for Data | |
Fitting a Line to Data: The Kalama Study | |
Reinitializing the Independent Variable | |
Interpolation and Extrapolation: Making Predictions | |
Looking for Links between Education and Earnings: Using Regression Lines | |
Using U.S. Census Data | |
Summarizing the Data: Regression Lines | |
Regression Line: How good a fit? | |
Interpreting Regression Lines: Correlation vs. Causation | |
Raising More Questions: Going Deeper | |
Chapter Summary | |
Check Your Understanding | |
Chapter 2 Review: Putting it all Together | |
Having it Your Way | |
A Case Study on Education and Earnings | |
When Lines Meet: Linear Systems | |
Interpreting Intersection Points: Linear and Non-linear Systems | |
When Curves Collide: Non-linear Systems | |
When Lines Meet: Linear System | |
Visualizing and Solving Linear Systems | |
Visualizing Linear Systems | |
Strategies for Solving Linear Systems | |
Linear Systems in Economics: Supply and Demand | |
Reading between the Lines: Linear Inequalities | |
Above and Below the Line | |
Reading between the Lines | |
Manipulating Inequalities | |
Breakeven Points: Regions of Profit or Loss | |
Systems with Piecewise Linear Functions: Tax Plans | |
Graduated vs. Flat Income Tax | |
Comparing the Two Tax Models: Flat vs. Graduated Plans | |
Chapter Summary | |
Check Your Understanding | |
Chapter 3 Review: Putting it all Together | |
Flat vs. Graduated Income Tax: Who Benefits? | |
A Comparison of Hybrid and Conventional Automobiles | |
The Laws of Exponents and Logarithms: Measuring the Universe | |
The Numbers of Science: Measuring Time and Space | |
Powers of 10 and the Metric System | |
Scientific Notation | |
Positive Integer Exponents | |
Exponent Rules | |
Common Errors | |
Estimating Answers | |
Zero, Negative and Fractional Exponents | |
Zero and Negative Exponents | |
Fractional Exponents | |
Converting Units | |
Converting Units within the Metric Systems | |
Converting between the Metric and English Systems | |
Using Multiple Conversion Factors | |
Orders of Magnitude | |
Comparing Numbers of Widely Differing Sizes | |
Orders of Magnitude | |
Graphing Numbers of Widely Differing Sizes: Log Scales | |
Logarithms Base 10 | |
Finding the Logarithms of Powers of 10 | |
Finding the Logarithm of Any Positive Number | |
Plotting Numbers on a Logarithmic Scale | |
Chapter Summary | |
Check Your Understanding | |
Chapter 4 Review: Putting it all Together | |
The Scale and the Tale of the Universe | |
Growth and Decay: An Introduction to Exponential Functions | |
Exponential Growth | |
The Growth of E. coli Bacteria | |
The General Exponential Growth Function | |
Doubling Time | |
Looking at Real Growth Data for E. coli Bacteria | |
Linear vs. Exponential Functions | |
General Forms: Linear and Exponential Function | |
Data Tables: Identifying Linear and Exponential | |
Finding the Equation for an Exponential Function | |
Comparing the Average Rates of Change | |
In the Long Run, Exponential Growth Will Always Outpace Linear Growth | |
Exponential Decay | |
The Decay of Iodine-131 | |
The General Exponential Decay Function | |
Half-Lives | |
Visualizing Exponential Functions | |
The Graphs of Exponential Functions | |
Horizontal Asymptotes | |
Exponential Functions: A Constant Percent Change | |
Exponential Growth: Increasing by a Constant Percent | |
Exponential Decay: Decreasing by a Constant Percent | |
Revisiting Linear vs. Exponential Functions | |
More Interesting Examples of Exponential Growth and Decay | |
Fitting a Curve | |
Doubling Time and Half-Life: Translating between Forms | |
The "Rule of 70" | |
The Malthusian Dilemma | |
Forming a Fractal Tree | |
Compound Interest and the Number e | |
Compounding at Different Intervals | |
Continuous Compounding Using e | |
Exponential Functions Base e | |
Converting ek into a | |
Semi-log Plots of Exponential Functions | |
Chapter Summary | |
Check Your Understanding | |
Chapter 5 Review: Putting it all Together | |
Computer Viruses | |
Logarithmic Links: Logarithmic and Exponential Functions | |
Using Logarithms to Solve Exponential Equations | |
Estimating Solutions to Exponential Equations | |
Rules for Logarithms | |
Solving Exponential Equations | |
Solving for Doubling Times and Half-Lives | |
Using Natural Logarithms to Solve Exponential Equations Base e | |
The Natural Logarithm | |
Returning to Doubling Times and Half-Lives | |
Visualizing and Applying Logarithmic Functions | |
The Graphs of Logarithmic Functions | |
Logarithmic Growth | |
Explore & Extend 6.3: Visualizing Logarithmic Functions | |
Stretching, Compressing and Reflecting | |
The Relationship between Logarithmic and Exponential Functions | |
Logarithmic vs. exponential growth | |
Logarithmic and exponential functions are inverses of each other | |
Applications of Logarithmic Functions | |
Measuring acidity: The pH scale | |
Using Semi-log Plots to Construct Exponential Models for Data | |
Why Do Semi-Log Plots of Exponential Functions Produce Straight Lines? | |
Chapter Summary | |
Check Your Understanding | |
Chapter 6 Review: Putting it all Together | |
Properties of Logarithmic Functions | |
Power Functions | |
The Tension between Surface Area and Volume | |
Scaling Up a Cube | |
Size and Shape | |
Direct Proportionality: Power Functions with Positive Powers | |
Direct Proportionality | |
Properties of Direct Proportionality | |
Direct Proportionality with more than one Variable | |
Visualizing Positive Integer Powers | |
The Graphs of f(x)=x 2 and g(x)=x 3 | |
Explore & Extend 7.3: Visualizing Power Functions | |
Odd vs. Even Powers | |
Symmetry | |
The Effect of the Coefficient k | |
Comparing Power and Exponential Functions | |
Which Eventually Grows Faster, a Power Function or an Exponential Function? | |
Inverse Proportionality: Power Functions with Negative Integer Powers | |
Inverse Proportionality | |
Properties of Inverse Proportionality | |
Explore & Extend 7.5: Designing Stringed Instruments | |
Inverse Square Laws | |
Visualizing Negative Integer Power Functions | |
The Graphs of f(x)=x^-1 and g(x)=x^-2 | |
Odd vs. Even Powers | |
Asymptotes | |
Symmetry | |
Explore & Extend 7.6: Finding Symmetries | |
The Effect of the Coefficient k | |
Using Logarithmic Scales to Find the Best Functional Model | |
Looking for Lines | |
Why is a Log-Log Plot of a Power Function a Straight Line? | |
Translating Power Functions into Equivalent Logarithmic Functions | |
Analyzing Weight and Height Data | |
Using a standard plot | |
Using a semi-log plot | |
Using a log-log plot | |
Explore & Extend 7.7: Constructing Functions from Log-Log Plots | |
Allometry: The Effect of Scale | |
Chapter Summary | |
Check Your Understanding | |
Chapter 7 Review: Putting it all Together | |
Scaling Objects | |
Quadratics and the Mathematics of Motion | |
An Introduction to Quadratic Functions: The Standard Form | |
The Simplest Quadratic | |
Designing parabolic devices | |
The Standard Form of a Quadratic | |
Properties of Quadratic Functions | |
Estimating the Vertex and Horizontal Intercepts | |
Visualizing Quadratics: The Vertex Form | |
Stretching and Compressing Vertically | |
Reflections across the Horizontal Axis | |
Shifting Vertically and Horizontally | |
Using Transformations to Get the Vertex Form | |
The Standard Form vs. the Vertex Form | |
Finding the Vertex from the Standard Form | |
Converting between Standard and Vertex Forms | |
Finding the Horizontal Intercepts: The Factored Form | |
Using Factoring to Find the Horizontal Intercepts | |
Factoring Quadratics | |
Using the Quadratic Formula to Find the Horizontal Intercepts | |
The discriminant | |
Imaginary and complex numbers | |
The Factored Form | |
The Mathematics of Motion | |
The Scientific Method | |
Deriving an Equation Relating Distance and Time | |
Velocity: Change in Distance over Time | |
Acceleration: Change in Velocity over Time | |
Deriving an Equation for the Height of an Object in Free Fall | |
Working with an Initial Upward Velocity | |
The Average Rate of Change of a Quadratic Function | |
Chapter Summary | |
Check Your Understanding | |
Chapter 8 Review: Putting it all Together | |
How Fast are You? Using a Ruler to Make a Reaction Timer | |
New Functions from Old | |
Transforming a Function | |
Transformations | |
Stretching, compressing and shifting | |
Reflections | |
Symmetry | |
Combining Two Functions | |
The Algebra of Functions | |
Polynomial Functions | |
Rational Functions | |
A Final Example | |
Chapter Summary | |
Check Your Understanding | |
Chapter 9 Review: Putting it all Together | |
Appendix: Student Data Tables for Exploration 2.1 | |
Data Dictionary for FAM1000 Data | |
Solutions | |
Table of Contents provided by Publisher. All Rights Reserved. |