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:
A = (∞, 2]
B = (2, 1)
C = [1, 2]
D = (2, 4]
E = (4, ∞)
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.

References
 McAdams, David E.. All Math Words Dictionary, step function. 2nd Classroom edition 201501084799968. pg 171. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
 Piecewise Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 11/19/2009. https://www.allmathwords.org/en/p/piecewisefunction.html.
Cite this article as:
McAdams, David E. Step Function. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/s/stepfunction.html.
Image Credits
Revision History
5/7/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/10/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
7/18/2018: Changed title to common format. (
McAdams, David E.)
11/19/2009: Initial version. (
McAdams, David E.)