**Representation of functions :**

Here we are going to see "How to represent a function"

A function can be represented in the following four ways.

(i) A set of ordered pairs :

Let f : A ---> B

The set f = { (a , b) / a ∈ A and b ∈ B } of all ordered pairs represents the function

(ii) A table :

The elements of A and their respective images under f can be given in the form of a table.

(iii) An arrow diagram :

An arrow diagram indicates the elements of the domain of f and their respective images by means of arrows.

(iv) A graph :

The ordered pairs in the collection f are plotted as points (x, y) in the x-y plane. The graph of f is the totality of all such points.

**Example : **

Let A = { 0, 1, 2, 3 } and B = { 1, 3, 5, 7, 9 } be two sets. Let f : A ---> B be a function given by f (x) = 2x + 1. Represent this function as (i) a set of ordered pairs (ii) a table (iii) an arrow diagram and (iv) a graph.

**Solution :**

(i) A set of ordered pairs :

Here "x" ------> elements of A and f(x) ------> elements of B

Then, we have

f(0) = 2(0) + 1 = 0 + 1 = 1 -------> (0, 1)

f(1) = 2(1) + 1 = 2 + 1 = 3 -------> (1, 3)

f(2) = 2(2) + 1 = 4 + 1 = 5 -------> (2, 5)

f(3) = 2(3) + 1 = 6 + 1 = 7-------> (3, 7)

The given function f can be represented as a set of ordered pairs as

f = { (0, 1), (1, 3), (2, 5), (3, 7) }

(ii) A table :

Let us represent f using a table as shown below.

(iii) An arrow diagram :

(iv) A graph :

If the order pairs are written as points in the form (x, y), we will get the points (0, 1), (1, 3), (2, 5) and (3, 7).

These points are plotted on the x-y plane as shown below.

The totality of all points represent the graph of the function.

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