Question

Does the equation `x^2+y=36` define `y` as a function of `x`?

Answer 1

Yes

Explanation:

Given:

`x^2+y=36`

By subtracting `x^2` from both sides of the equation (a reversible operation), we get the equivalent equation:

`y = 36-x^2`

In this form it is clear that given any value of `x`, the equation determines a unique value of `y`.

So it is a function with domain the whole of `(-oo, oo)`.

graph{y = 36-x^2 [-10, 10, -52, 52]}