Definition of Step Function
A step function is a special type of function whose graph is a series of line segments.
The graph of a step function looks like a series of small steps.
Video Examples: The Unit Step Function
Example of Step Function
The figure below shows the graph of the step function f(x) = [[x - 1]], which is a greatest integer function.
Another name for this kind of graph is a piecewise linear graph, because the graph consists of small line segments.
Solved Example on Step Function
Ques: Which of the following is a step function?
(i) f(x) = b
(ii) f(x) = |x|
(iii) f(x) = [[x]]
A. only (i)
B. only (ii)
C. only (iii)
D. all the three
Correct Answer: C
Step 1: Among the functions listed, only f(x) = [[x]] is the step function.
[[ ]] indicates that its a Greatest Integer Function that rounds any number down to the nearest integer.
Step 2: So, f(x) = [[x]] is a step function.