**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, onlyf(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