Types Of Function ?

Types Of Function ? You can free Read AND Download Best Article About Types Of Function .

You can free Read AND Download Best Article About Types Of Function .

About  Types Of Function:

Some important types of function are given below:

1-Algebraic Functions:

Algebraic function are those functions which are defined by algebraic expressions. Now we classify algebraic functions as follows:

1.1Polynomial Function    

A function P of the form p(x)=a⏻nx⏻n+an-1+x⏻n-1+............a1x+a0for all of x,where the coefficient a⏻n,an-1,an-2,.......a2,a1,a0 are all real numbers and exponents are non-negative integers ,is called Polynomial Function.
The domain and range of P(x) are, in general,subsets of real numbers.

If a⏻n≠0,then P(x) is called a polynomial function of degree n and a⏻n is leading co-efficient of P(x).                                                                                                                1.2 Linear Function

 If the degree of a polynomial function is 1,it is called a Linear Function.
A linear function is of the form :f(x)=ax+b (a≠0),a,b are real numbers.

For Example:

f(x)=3x+4 or y=3x+4 is a linear function.Its domain and range are the set of real numbers.

1.3 Identity Function :

For any set X,a function I:X→X Of the form I(x)=x ∀ x ∈ X ,is called an Identity Function.Its domain and range is the set X itself.In particular, ifX=R, then I(x)=x, for all x ∈ R,is the identity function.

1.4 Constant function
Let X and Y be sets of real numbers.A function C:X→Y defined by
C(x)=a , ∀ x ∊ X ,a ∊ Y and fixed,is called a Constant function .
For Example:
C:R → R defined by C(x)=2 ,∀ x ∈ R is a constant function.
1.5 Rational  Function
A function R(x) of the form P(x)-Q(x), where both P(x) and Q(x) are polynomial functions and Q(x)≠0,is called a  Rational  Function .
The domain of a rational function R(x) is the set of all real numbers x for which Q(x)≠0.

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