How to Graph the Greatest Integer Function in Geometer's Sketchpad

The greatest integer function, also called the floor function, creates a step function when graphed. This function requires the largest integer that is equal to or greater than "x." The greatest integer function of a real number, "x," is represented by [x] or |_x_|. Geometer's Sketchpad is a software program that has a graphing capability. However, the program does not have the ability to automatically graph an equation. You must first determine the coordinates you wish to place on your graph, and then use the tools on Sketchpad to create the graphed function.

Instructions

1. Find the coordinates to plot on the graph using the equation provided. For example, if the equation is y = [x], "y" equals 1 if "x" equals 1.3, since it is the closest integer rounded down. So in this same example, if x = 1.9, then "y" is still 1. This can be tricky on negative numbers. For example, if x = -1.2, then "y" equals -2 because of the rounding down to the nearest whole integer.

2. Select "Graph" on the top tool bar of Geometer's Sketchpad, and then select "Define Coordinate System" to display a number graph on the screen.

3. Select the "." tool that is located on the left tool bar, and then place the first point on the graph at the lowest coordinate points. For example, in the equation y = [x], if "x" is zero, "y" is also zero. If "x" = -1, "y" also equals -1. Place a point at this coordinate on the graph.

4. Select the circle tool that is on the left tool bar and draw a small circle at the next greater integer from the point on the "x" axis. If the first coordinate is at (0,0), place the circle at 1. This is because in the equation y = [x], all values for "x" between 0 and .99 still equal zero on the "y" axis. The circle indicates that the whole integer is not part of the graph.

5. Select the segment tool on the left tool bar and draw a line segment between the point and the circle.

6. Select the cursor symbol on the left tool bar. The circle and line segment create two separate points on the second coordinate created on the graph. Place your cursor over each point, right click, and then select "Hide Point" to remove the point from view on the graph.

7. Repeat the steps for each value for "x." For example, in the equation y = [x], if "x" equals 1.4, "y" equals 1. Place the first point (1,1), make a small circle at (2,1) and make a line segment between those two points. The resulting graph will look like a staircase moving up as the graph progresses left to right.

References

• I Coach Math: Back to Math Dictionary Greatest Integer Function
• YouTube: Graphing the Greatest Integer or Floor Function