Question

Which of the relations below is not a function?

Mark all that apply.
A) {(2,5), (3,9), (4,13), (5.17)}
B) {(3,4), (4,5), (3,6). (6,7)}
C) {(1,1), (2,2), (3,3), (4,4)}
D) {(3,4), (4,5), (5,6)}
E) {(3,4), (4,5), (4,6}}

Answer 1

Relations B and E do not represent the function.

Explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

If we closely observe relation B, and E i.e.

• B) {(3,4), (4,5), (3,6). (6,7)}

• E) {(3,4), (4,5), (4,6)}

Relation 'B' IS NOT A FUNCTION

Relation B has duplicated or repeated inputs i.e. x = 3 appears twice times. we can not have duplicated inputs as there should be only 1 output for each input.

Thus, relation B is NOT a function.

Relation 'E' IS NOT A FUNCTION

Relation E has duplicated or repeated inputs i.e. x = 4 appears twice times. we can not have duplicated inputs as there should be only 1 output for each input.

Thus, relation B is NOT a function.

Therefore, relations B and E do not represent the function.