Step Function
Pronunciation: /stɛp ˈfʌŋk ʃən/ Explain

Figure 1: Step function.

A step function is a
piecewise function
that is
constant
over a
finite
number of
intervals.
A step
function
can also be called a staircase function.
A step function is piecewise. Over each of the 'pieces', each interval over the
domain,
the value of the function remains constant. Figure 1 shows a step function with five intervals
labeled
A,
B,
C,
D and
E as follows:
Over each of those intervals, the value of
f(x) is constant. For example, over interval
C,
f(x) = 2.
Examples of functions that not step functions

This function is not a step function because it is not constant on the interval [1,1].


Figure 4: Not a step function.
 Figure 5: Not a step function.

More Information
 Piecewise Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 11/19/2009. http://www.allmathwords.org/en/p/piecewisefunction.html.
Cite this article as:
McAdams, David E. Step Function. 7/18/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/stepfunction.html.
Image Credits
Revision History
7/18/2018: Changed title to common format. (
McAdams, David E.)
11/19/2009: Initial version. (
McAdams, David E.)