# Functions

### Absolute Value Functions

﻿The absolute value (ABS) function is the positive value of a number or quantity. Its graph has a very peculiar shape, a V. Since absolute… Read more

### Absolute Value Polynomials

What would you guess the absolute value of a polynomial function would look like? Try some here. I think you will be very surprised. Can… Read more

### CO2 Growth

Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will focus mainly on climate change… Read more

### Composition of Functions

One of the most powerful aspects of the mathematics of functions is our ability to treat them as abstract quantities (essentially numbers) and then combine… Read more

### Exploring Triangles

Create, manipulate, and explore triangles in this live interactive spreadsheet. On the surface, a triangle is being drawn on a graph, but the real magic… Read more

### Exponential Functions

What if you created a function where the exponent is a variable? As you might expect, this would be called an exponential function. When you… Read more

### GDP

The GDP or Gross Domestic Product of a country is one measure of its wealth. What can this data tell us about the U.S. economy?… Read more

### Graphing

Graphs as we know them were first invented by Galileo. They are powerful images of functions. I will introduce you to graphs by letting you… Read more

### Hindu Algebra Problem

This problem is typical of the earliest algebra problems that likely came out of India. It is interesting historically, and it is the kind of… Read more

### Interest

Which form of interest, simple or compound, is the fairest? If you were buying a house or a car which would you rather have, which… Read more

### Inverse of a Function

Spreadsheets make it very easy to switch axes and add graphs. They enable students to play with what may have been difficult and abstract concepts… Read more

### Inverse of Linear Functions

What does a linear function look like when we interchange the inputs and outputs, that is make the x-axis the y-axis and vice versa. Read more

### Inverse Variation

The variables in most of the functions we are used to working with vary directly, as one goes up the other goes up. What do… Read more

### Linear Functions

Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general… Read more

### Lissajous Figures

We often see Lissajous figures in old sci-fi movies because they are so cool. As you play with them I think you will find them… Read more

### Magic Number (Infinite Series)

What if you made a series of unit fractions with the odd numbers as their denominator, added the first two together, subtracted the next one,… Read more

### Moore’s Law

It was one of the most amazing visions of the future ever made. In 1965 Gordon Moore, one of the founders of Intel, proposed a… Read more

### Motion Problems

George is in New York and Martha is in Washington. They leave at the same time and follow the same road to meet each other… Read more

### Normal Distribution

Most museums with math exhibits have a Pascal’s triangle made up of pegs with balls falling down between them and bouncing off of them. One… Read more

### Parametric Equations

Parametric equations are powerful tools to model projectile motions and to graph things that are not functions like circle or ellipses. The x and y… Read more

### Parentheses and Pi

Parentheses are very important in spreadsheets because like all programming, spreadsheet formulas have to be very specific. A big formula, especially one like Viete’s approximation… Read more

### Pascal’s Triangle

Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that adds the two cells in… Read more

### Polynomial Functions

Polynomial functions are not limited to the highest term and while that term is most important in determining the shape of its graph, additional terms… Read more

### Power Functions

Adding an exponent, sometimes referred to as a ‘power’, to the input variable of a linear function that passes through the origin creates a power… Read more

### Projectile Motion

Let’s do a little target practice with this spreadsheet projectile simulator, which will map out the flight path of an arrow shooting toward a target. Read more

What does each of the coefficients do? How does it change the graph of the parabola. What does a do, what does c do and… Read more

### Rate of Growth

We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or slower today. Is it out… Read more

### Rule of 72

The rule of 72 is an old banker’s rule of thumb to find out how long it will take to double your money at different… Read more

### Sine Function

Spreadsheets are not limited to algebraic functions, they can also display trigonometric functions. We are modeling the sine function, but you can try any of… Read more

### Solar System

When I was young I loved to play with planetary data, to explore their patterns, to learn more about astronomy, and to deal with large… Read more

### Solving Equations Digitally

This Lab introduces a method for solving or estimating the solution to an equation digitally that can be applied to many types of equations. This… Read more

### Syracuse Problem

I built a Lab for you to play with the Syracuse Problem and to learn to use spreadsheets to play with like problems in fun… Read more

### Systems of Equations

Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable… Read more

### The Chessboard

We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2… Read more

### Triangular Numbers

1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and… Read more

### What is x?

What is “x”? Or how do we represent variables and functions on spreadsheets? Read more