Types of Functions:

Constant Function:
            Let 'A' and 'B' be any two non–empty sets, then a function '' from 'A' to 'B' is called Constant Function if and only if range of '' is a singleton.
                        OR;
            Let be a function then a function '' from 'A' to 'B' is called a constant function if , whose  is a constant.
            e.g.        
            
Algebraic Function:
            The function defined by algebraic expression are called algebraic function.
                                           e.g.  
Polynomial Function:
            A function of the form
Where 'n' is a positive integer and are real number 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 linear function is
                                                               
Quadratic Function:
            A polynomial function with degree '2' is called a Quadratic function.
The most general form of Quadratic equation is
                                                               
Cubic Function:
            A polynomial function with degree '3' is called cubic function.
The most general form of cubic function is
                                                               
Identity Function:
            Let be a function then '' is called on identity function. If .
Rational Function:
            A function defined by , where both andare polynomial function is called, rational function.
Trigonometric Function:
            A function, etc, then  is called trigonometric function.
Exponential Function:
            A function in which the variable appears as exponent (power) is called an exponential function
                e.g.           (i)         (ii) .

Logarithmic Function:
            A function in which the variable appears as an argument of logarithmic is called logarithmic function.
                e.g.           .
Hyperbolic Function:
            The following are hyperbolic functions:

Inverse Hyperbolic Functions:
            The following are inverse hyperbolic functions:

Explicit Function:
            When the dependent function is expressed clearly in terms of the independent variables, the function is said to be explicit function.
                                e.g.            etc.
Implicit Function:
            An implicit function is that which contains two or more variables that are not independent of each other.
                                e.g.          
                                                          etc.
Parametric Function:
            A function in which 'x' and 'y' are expressed as functions of 3rd variables is called a parametric function.
                                                In term of same variables.
Example:
            Show that the parametric equations  and  represent the equation.
Solution:
                We have
            ——————— (1)
            ——————— (2)
            Squaring and adding (1) and (2)
                We have
                          
              
             
            But
                 

           

Even Function:
            A function is said to be an even function, if
            
e.g.          
            Replace 'x' by ''
            
                                                                                                                                                                                            
         
            It is an even function.
Odd Function:
            A function is said to be an odd function if
               
e.g.          
                Replace 'x' by ''
               
                               
         

(Examples of Functions)

Function and Limits

(Nature of Functions)