Question

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

Yes, the range value 3 corresponds to two domain values, 1 and 2.
Yes, there is no value in the domain that corresponds to more than one value of the range.
No, there is no value in the domain that corresponds to more than one value of the range.
No, the range value 3 corresponds to two domain values, 1 and 2.

Answer 1

"Yes, there is no value in the domain that corresponds to more than one value of the range."

Explanation:

Recall that for a relationship to be a function, each element of the domain should have only one associated value in the range.

So in the example given in coordinate pair form: {(1, 3), (-4,0), (3, 1), (0, 4), (2, 3)}

notice that:

the element 1 in the Domain relates to 3 in the Range,

the element -4 of the Domain relates to 0 in the Range,

the element 3 in the Domain relates to the number 1 in the Range,

the element 0 in the Domain relates to 4 in the Range,

and finally the element 2 in the Domain relates to 3 in the Range.

Each of the elements in the Domain, relate to one and only one element in the Range. The fact that one of the related values is repeated is not an obstacle for the relationship to be a function.

The correct answer therefore is:

"Yes, there is no value in the domain that corresponds to more than one value of the range."