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.
      Step 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]]
    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.

Translate :