Question

Is the following relation a function?

two ovals, one labeled x and the other labeled y. The negative 2 in the x oval is pointing to the 3 in the y oval, the 0 in x is pointing to 1 in y, 5 in x pointing to 8 in y, and 7 in x pointing to 5 in y

Answer 1

Yes, because each x maps uniquely to a value in y.

Answer 2

Yes, the given relation is a function.

Because every element of the set x has a single image.

Explanation:

Relation--

A relation from the set A to set B is the collection or set of all the ordered pair of the type: (a,b)

where a belongs to A and b belongs to B.

Function--

A relation from a set A to set B is a function if every element of A is mapped to some element of B and there is just one image corresponding to each element of x.

Now after looking at the mapping diagram we observe that no element of A is mapped to two elements of B.

i.e. every element has a single image.

Hence, the relation is a function.