the graph & nature of the greatest integer function [x], absoulte value function modulus of x.

• Greatest Integer Function is a step function written as f(x) = [x], where f(x) is the greatest integer less than or equal to x.
• In other words, a greatest integer function rounds any number down to the nearest integer.

Examples

• The greatest integer less than or equal to the number [5.3] is [5].

• The greatest integer less than or equal to the number [- 5.3] is [- 5].

   

  The graph of the greatest integer function is a step function.

  

   

  the absolute value or modulus of x is:

  | x| = -x if x is strictly less than 0

  and it equal to +x if x0

  the graph of modulous function is