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

Yes; although the Domain of $x$ will be limited (assuming by "function" we mean a "real value function")
${y}^{2} = 3 x - 7$ can be re-written as
$y = \sqrt{3 x - 7}$
which gives a unique value provided $x \ge \frac{7}{3}$
If $x < \frac{7}{3}$ this equation gives an Imaginary value for y, so it is still a function; it is just not a real valued function).