Is the relation {(1, 3), (-4, 0), (3, 1), (0, 4), (2, 3)} a function? Why or why not?

Solution:

R = {(1, 3), (-4, 0), (3, 1), (0, 4), (2, 3)}

We know that

Here the first element makes the domain and the second element makes the range

Domain D = {1, -4, 3, 0, 2}

Range R = {3, 0, 1, 4, 3}

A relation will be a function if each domain value corresponds to one and only value in the range.

In set R, each element has only one pre-image.

Given relation ‘R’ is a function

Therefore, the relation {(1, 3), (-4, 0), (3, 1), (0, 4), (2, 3)} is a function.

Is the relation {(1, 3), (-4, 0), (3, 1), (0, 4), (2, 3)} a function? Why or why not?

Summary:

The {(1, 3), (-4, 0), (3, 1), (0, 4), (2, 3)} is a function. A relation will be a function if each domain value corresponds to one and only value in the range. In set R, there is no domain value which corresponds to one and only value in the range.