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Question

# Among the following, represents a function.

A
Option III
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B
Option I
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C
Option II
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D
Option IV
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Solution

## The correct option is A Option IIIWe know, if every input has exactly one output, then we can call this relation a function. Let's consider the mapping diagram in Option I. (1,9) and (5,8) have exactly one input related to one output. Also (3,10) and (3,11) have one input related to two output. So, it is not a function. Now, let's consider the mapping diagram in Option II. (1,C) and (2,D) have exactly one input related to one output, but (3,A) and (3,B) have one input related to two output. So, it is not a function. Let's consider the mapping diagram in Option III. The ordered pairs are (A,1), (B,2), (C,1), and (D,3). (A,1) and (C, 1) have both the inputs related to one output. (B, 2) and (D, 3) has one input related to one output. So, this diagram represents a function. Now, finally consider the mapping diagram in Option IV. (A, 1) (B, 2) and (C, 3) have exactly one input to related one output. Here, D is not mapped with any output. So, this diagram is not a function. So, only diagram in Option III represents a function.

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