Question

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.

Answer 1

A = {0, 1, 2, 3}, B = { 1, 3, 5, 7, 9 },f(x) = 2x + 1

f(0) = 2(0) + 1 = 1, f(1) = 2(1) + 1 = 3 ,f(2) = 2(2) + 1 = 5, f(3) = 2(3) + 1 = 7

(i) Set of ordered pairs 

The given function/can be represented as a set of ordered pairs as f = {(0, 1), (1, 3), (2, 5), (3,7)}

(ii) Table form
Let us represent f using a table as shown below.

x	0	1	2	3
f(x)	1	3	5	7

(iii) Arrow Diagram

Let us represent f by an arrow diagram.

We draw two closed curves to represent the sets A and B. Here each element of A and its unique image element in B are related with an arrow.

(iv) Graph

We are given that

f = {(x,f(x)) | x ∈ A} = {(0,1), (1, 3), (2, 5), (3, 7)}. Now, the points (0, 1), (1, 3), (2, 5) and (3, 7) are plotted on the plane as shown below.

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