If K = (x, y), is Set K a function?

1.

The description of set K as (x, y), means the following:

the elements of set K are pairs (x, y)

such that: x-y=5, that is we can write (x, y) = (x, x-5).

2.

A set of (ordered) pairs is a function, if each of the first coordinates is paired to only 1 specific value, not 2 or more.

for example: { (1,2), (3, 5), (3, 8) } is not a function because 3 is not paired to only one second value, we have (3, 5) but also (3, 8).

whereas, { (-2, 4), (3, 5), (8.1, 17) } is a function, because each first coordinate is unique, we don't see it again in another pair.

3.

Back in our set K, the description of pairs (x, y) as (x, x-5)

makes sure that each x, produces a specific y, for example in K we have:

(5, 0), and we cannot have (5, a value ≠0), because it would not fit the description (x, x-5)

Answer: yes