Step Function
A step function is a discontinuous function whose graph consists of half-open intervals. It is often called the greatest integer function (denoted 
). The greatest integer function rounds a number down to the nearest integer. If the number is an integer use that integer. If the number is not an integer use the next smaller integer.
Example:
Find 
.
The largest integer not larger than 4 is 4.
So, f(x) = 4.
Find 
.
The largest integer not larger than 2.8 is 2.
So, f(x) = 2.
Find 
.
The largest integer not larger than –3.4 is –4.
So, f(x) = –4.
(Remember: –3 is larger than –4.)
