Tutorial Types of Functions


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 ''



It is an odd function.

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