Question

Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain.

Answer 1

Yes this is a function, since the `x` values are all distinct (a sufficient condition).

Explanation:

Given the set:

`{ (3, 5), (-4, 5), (-5, 0), (1, 1), (4, 0) }`

The domain is the set of `x` coordinates - that is the set of first elements of each pair:

`{ 3, -4, -5, 1, 4 }`

Notice that these are all distinct, hence the relation has exactly one `y` value (second element of a pair) for each `x` value in the domain.

So this is a function.

By way of contrast, the range of the relation is the set of `y` values:

`{ 5, 5, 0, 1, 0 } = { 0, 1, 5 }`

The `y` values are not all distinct, so the function is not one to one.