I learnt that one precondition for y=f(x) was, that to each x-value onlyone single y valueis 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?