Greatest Integer Function

The greatest integer function, denoted by int, is defined as follows:

int(x) = greatest integer less than or equal to x

The greatest integer function is found in the catalog.

To obtain a graph of the greatest integer function, press to access the equation editor. Enter y1 = int(x) as follows:

press CATALOG
press I (located above the 9 key)
select int (
press
type X )
press

The function y1=int(x) is entered into the equation editor.

We are now ready to view a graph of the greatest integer function. Press to access the Zoom menu. Press 6 to select 6: ZoomStd. One then obtains the graph shown at the right. In this graph, the steps of the int function are inappropriately connected.

To obtain a correct graph, we must change from the Line style to the Dot style. Press to return to the Y= menu. Highlight y1=int(x). With int(x) highlighted, press to access the Style menu (F6 is located above the F1 key). Press to select 2: Dot. Press ENTER twice (once to enter the dot style, and again to enter the function). Press to access the Zoom menu, then press to select 6: ZoomStd. The steps in the graph of the greatest integer function are now disconnected.

For a better view, press to access the Zoom menu, then press to select 5: ZoomSqr. From the zoom square presentation, press to access the Zoom menu again, then press to select 2:ZoomIn. Press in response to the prompt New Center? to zoom in from the origin. Then press either or to clear the extraneous information from the graph. If needed, reset the WINDOW with xscl = 1 and yscl = 1 to obtain the graph displayed at the right. Note that the step from is occluded by the x-axis.