Vernier Software & Technology

# Stepping to the Greatest Integer: The Greatest Integer Function

## Introduction

Not all mathematical functions have smooth, continuous graphs. In fact, some of the most interesting functions contain jumps and gaps. One such function is called the greatest integer function, written as y = int x. It is defined as the greatest integer of x equals the greatest integer less than or equal to x. For example, int 4.2 = 4 and int 4 = 4, while int 3.99999 = 3.

In this activity, you will create a function similar to the greatest integer function graph by having a group of students stand in a line in front of a Motion Detector and then step aside one by one. The equation for this graph, in the general form, is

${\text{y = A int (Bx) + C}}$

You can find appropriate values for the parameters A, B, and C so that the model fits the data.

## Objectives

• Use a Motion Detector to collect position data showing evenly-spaced jumps in value.
• Model the position data using the greatest integer function.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Option 2

You may also need an interface and software for data collection. What do I need for data collection?