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.

Examples 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

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.

Related Terms for Step Function

  • Function
  • Line Segment