Important Functions

1.   Absolute value function (modulus function):
= magnitude of or the positive value of .
The expression  can be further split as follows:
=

Greatest integer function (unit step function)

= the greatest integer less than or equal to .

It can also be simplified as:
if          where n is an integer.

Continuity

The graph of f (x) is discontinuous (i.e. break in the curve) at integral value of x.

Domain & Range

The Domain of the function  is  and Range is

Signum Function

=

This can also be written as

=

Exponential Function

where          or

This function is the inverse of logarithmic function i.e. it can be obtained by interchanging
by  in

As observed from the graph, if  then  increases as  increases.

If, then decreases as increases.

Continuity

The graph of
is continuous (i.e. no break in the curve) everywhere.

Domain & Range

The Domain of the function  is  and Range is.

Trigonometric Functions

If a function f (x) is symmetrical about origin i.e. f (x) =- f (-x) for all values of x, then the function y = f (x) is called an odd function.

Period

Period of   and  is

Period of  is