# How do you decide whether the relation #x - 3y = 2# defines a function?

##### 1 Answer

Mar 25, 2016

#### Explanation:

- Given:
#x-3y=2# - Required: Is the above relation a function?
- Solution Strategy: Use the standard deﬁnition of a function.

Let X and Y be sets. - A function
#f : X → Y# means that for every#x ∈ X# , there is a**unique**#f(x) ∈ Y# . We call the se X the domain of#f# .

The take home lesson here is that a **if and only if** for every value of

So we need to show that the function in your question uniquely maps

1) First write you equation in the form:

Now we see that for every

So we conclude that