**MATHMAA**

__ Function :__

Functions arise whenever one quantity depends on another. Consider the following situations.

1) The area A of a square depends on the length of the side S. Area of square (A)=S*S =S^2

Area of square changes as S changes. With each positive number S there is

associated one value of A, and we say that A is a function of S.

__Definition of Function :__

No two ordered pairs have same first co-ordinate.

Let \(f:A \mapsto B\) is said to be function if every \(x\epsilon A\)

has distinct image in B . Each element of A has distinct image in B. A

is called * domain* , B is called

are called * Range *of the function.

The most common method for visualizing a function is its * graph*.

If f is a function with domain A , then its graph is the set of ordered

pairs {(x, f(x))| \(x\epsilon A\)}.

Examples :

1) f={(1,2), (3,4), (5,9)} is a function as the first coordinates

{1,3,5} are distinct.

2) g={(1,a),(2,c),(2,d), (3, f)} is not a function as 2 has two images

c and d. 2 repeated more than once so g is not a function.

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