# 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 Step Functions  Figure 2: Ceiling function. Figure 3: Floor function.

### 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.

1. McAdams, David E.. All Math Words Dictionary, step function. 2nd Classroom edition 20150108-4799968. pg 171. Life is a Story Problem LLC. January 8, 2015. Buy the book

• 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.

McAdams, David E. Step Function. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/stepfunction.html.

### 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.)