Question 585845
{{{ y=x^2+6}}} defines y as a function of x, because for every x value there is no more than a y value. (In fact for every x there is exactly one y value). We can forgive a function if some values of x do not have a y, but if there is more than one y for even one value of x, then the relation is not a function.
{{{x=y^2-6}}} does not define y as a function of x, because some value(s) of x have more than one y. 
In general,
{{{x=y^2-6}}} --> {{{x+6=y^2}}} --> {{{y=sqrt(x+6)}}} or {{{y=-sqrt(x+6)}}} 
So, all the values of x larger than -6 would have two y values.
For example, x=10 would be paired with y=4 and y=-4.
A function cannot assign more than one y to any x value.