# Introduction To Functions.

**What is Function?**

A Function from set A to set B is a Relation or a rule which associates or maps or images each and every element of set A with a element in set B.

A function is a special case or Relation in which each and every element of first set (A) is related with only one element of second set(B).

**Denotation of function: **

A function from set A to set B is denoted by :

f:A→B

And read as “f is a function from set A to set B”. We use f,g,h and F,G,H mainly to denote a function.

If we take any element of Set A and process it through the function (or use the rule of given function in it) then the element of set A is changed or imaged to another element which is an element of set B.

we denote the above statement by:

f(x)=y

where “x” is a element of set “A” and “y” is the corresponding element of set “B”.

This means “x” becomes “y” when it is processed through the function “f”.

Like wise if we define a function “f” as “y is square of x”

then

f(x)=x^{2}

or, “x” becomes x^{2} when it is processed through the function or rule “f”.

So in the above example if set A={1,2,3} then when set “A” is processed through function “f” Set “A” is converted into another set(say B) where B={2,4,9}

A function can also be denoted by different graphical methods as given below.

If set A={1,2,3} is processed through a function “f” which is defined by “y is square of x” or,

f:A→B or y=f(x)=x^{2}

then we can denote this function using following method:

** a> Table Method.**

**b>Arrow Diagram method:**

**c>Graph method:**

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**Domain and range of a Function:**

Domain of a Function is the set of elements which are processed or to be processed by a function.

and Range is the set of elements which are produced after processing the domain of a Function.

For example:

If set A={1,2,3} and set A is to be processed by function “f” to produce another set B={1,8,27}

or f:A→B

Then set “A” is the domain of function “f” and set “B” is the range of function “f”.

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