1. Step Functions

3. Graph :

5. Special Step Functions
Two particular kinds of step functions are called ceiling functions ( f (x)= and floor functions ( f (x)= ).
In a ceiling function, all nonintegers are rounded up to the nearest
integer.
An example of a ceiling function is when a phone service company charges by the number of minutes used and always rounds up to the nearest integer of minutes.

6. Special Step Functions
In a floor function, all nonintegers are rounded down to the nearest integer.
The way we usually count our age is an example of a floor function since we round our age down to the nearest year and do not add a year to our age until we have passed our birthday.
The floor function is the same thing as the greatest integer function which can be written as f (x)=[x].