I learnt that one precondition for y=f(x) was, that to each x-value only one single y value is assigned, so that no double solution are accepted.
Imagine now
-y(y+8)=(x-3)^2 -8. This fuction will result in a circle, which means that to some x values, two y values are assigned.
How ist that possible, respectively, did i missunderstood the rules concerning functions?