# Types of Functions

__Constant Function:__

Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘’ from ‘A’ to ‘B’ is called a constant function if and only if the range of ‘’ is a singleton.

__Algebraic Function:__

A function defined by an algebraic expression is called an algebraic function.

e.g.

__Polynomial Function:__

A function of the form

where ‘n’ is a positive integer and are real numbers is called a polynomial function of degree ‘n’.

__Linear Function:__

A polynomial function with degree ‘’ is called a linear function. The most general form of a linear function is

__Quadratic Function:__

A polynomial function with degree ‘2’ is called a quadratic function. The most general form of a quadratic equation is

__Cubic Function:__

A polynomial function with degree ‘3’ is called a cubic function. The most general form of a cubic function is

__Identity Function:__

Let be a function then ‘’ is called an identity function if .

__Rational Function:__

A function defined by , where both and are polynomial functions is called a rational function.

__Trigonometric Function:__

A function , etc., then is called a trigonometric function.

__Exponential Function:__

A function in which the variable appears as an exponent (power) is called an exponential function

e.g. (i) (ii) .

__Logarithmic Function:__

A function in which the variable appears as an argument of a logarithm is called a logarithmic function.

e.g. .