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)       

(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

Additional Links for Step Function

• Click here for samples
• Back to Mathematics Dictionary