Question

1. Which relation is a function?

(Points : 4)
{(1, 2); (2, 3); (3, 4); (1, 5)}
{(1, 2); (1, 3); (1, 4); (1, 5)}
{(1, 2); (2, 3); (3, 4); (2, 5)}
{(1, 2); (2, 2); (3, 2); (4, 2)}

Answer 1

{(1, 2); (2, 2); (3, 2); (4, 2)} because for each x, there's only one corresponding y.

Answer 2

The correct option is 4.

Explanation:

A relation is called a function if there exist a unique value of y for each value of x.

If means if a relation is defined as (x,y), then for each value of x there exist a unique value of y.

In option 1, at x=1, the values of y are 2 and 5.

Since there exist more than one values of y for a single value of x, therefore option 1 is incorrect.

In option 2, at x=1, the values of y are 2, 3, 4 and 5.

Since there exist more than one values of y for a single value of x, therefore option 2 is incorrect.

In option 3, at x=2, the values of y are 3 and 5.

Since there exist more than one values of y for a single value of x, therefore option 3 is incorrect.

In option 4, for each value of x, there exist single value of y, therefore option 4 is correct.