Question

Is `xy = 7` a function?

Answer 1

If `x` and `y` are related by `xy = 7`, the `y` is a function of `x`.

Explanation:

Solve the equation for `y`.

We get `y = 7/x`

Now ask yourself: If I choose an `x`, do I ever get two different numbers for `y`? If the answer is NO, the `y` is a function of `x`.

In this case the answer IS no, so, `y` is a function of `x`.

For comparison

If `x` and `y` are related by `x+y^2 = 3`, then `y` is NOT a function of `x`.

When we solve for `y`, we get:

`y^2 = 3-x" "` so

`y = +-sqrt(3-x)`

Now, if I put in a number for `x`, I (usually) get TWO numbers for `y`. (except when `x=3`).
But if I EVER get two numbers (even just for one single solitary `x`) then `y` is NOT a function ox `x`.

So for `x+y^2 = 3`, we end up with: `y` is not a function of `x`.