a function is (always, never or sometimes) a relation.

always

a relation is sometimes a function

Is a relation always a function

To determine whether a function is always, never, or sometimes a relation, let's start by defining both terms.

A relation is a set of ordered pairs (x, y) where x is the input and y is the output. In other words, a relation is a collection of pairs that associates elements from one set with elements from another set.

A function, on the other hand, is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). In other words, for every x-value, there can be only one corresponding y-value.

With these definitions in mind, we can conclude that every function is, in fact, a relation. This is because a function is a special type of relation that meets the requirement of having a unique output for each input. So, the correct answer is "a function is always a relation."

To summarize:
- A relation is a more general term that includes any set of ordered pairs.
- A function is a specific type of relation that meets the requirement of having a unique output for each input.