Step Function
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.
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]]
Choices:
A. only (i)B. only (ii)
C. only (iii)
D. all the three
Correct Answer: C
Solution:

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.
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