Question

If `y^2=3x-7`, is y a function of x?

Answer 1

Yes; although the Domain of `x` will be limited (assuming by "function" we mean a "real value function")

`y^2 = 3x - 7` can be re-written as

`y = sqrt(3x - 7)`
which gives a unique value provided `x>= 7/3`

If `x < 7/3` this equation gives an Imaginary value for y, so it is still a function; it is just not a real valued function).