Question

Which set of ordered pairs is a function?

A. (1,2) (3,4) (5,6) (3,-4)
B. (8,4) (4,3) (2,2) (8,1)
C. (2,5) (3,10) (4,15) (5,20)
D. (2,4) (2,3) (2,1) (2,0)

Answer 1

OPTION C

Explanation:

An element in the domain should be mapped to exactly one element on the co-domain. Also, every element in the domain should be mapped to an element in the co-domain.

These two conditions are satisfied to call a relation, a function.

Two different elements in the domain can be mapped to the same element in the co-domain. But the same element in the domain cannot be mapped to two different elements in the co-domain.

A) (1,2), (3,4), (5,6), (3,-4)

Here, the element '3' is mapped to 4 and -4. So, this is not a function.

B) (8,4), (4,3), (2,2), (8,1)

'8' is mapped to 4 and 1. So, it is not a function.

C) (2,5), (3,10), (4,15), (5,20)

All the elements in the domain are mapped to an element in the co-domain. Also, every element in the domain has exactly one image in the co-domain. So, this relation is a function.

D) (2,4), (2,3), (2,1), (2,0)

The element '2' has more than one image. Clearly, it contradicts the definition of a function.

So, only OPTION C is the answer.