Question

How do you decide whether the relation `4x-7y=3` defines a function?

Answer 1

Explanation:

If you graph it, you can see that it is a straight linear function, as to be expected with an equation in the (rearranged) form `y=mx+c`. A good test when defining functions is the straight-line test: If you draw a straight vertical line down at any point through a graph of the function, you should only intersect with the function once - if you intersect with it more than once, it is not a function.

If there are no exponents in the equation, then it will always be a function, because there is no way that one can obtain two different answers for a single x-coordinate unless there are exponents involved.