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MATHMAA

# Function

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 Co-damain  and the outputs (images)

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.