Suppose you mean y = (x^2 + 9) / x
The maximum value of y is approached when x approaches zero from the right hand side.
The minimum value of y is approached when x approaches zero from the left hand side.
Note that neither value can ever truly be reached.
Suppose you mean y = x^2 + (9 / x) instead.
The maximum value of y is approached when x approaches zero from the right hand side, as well as when x approaches infinity or negative infinity.
The minimum value of y is approached when x approaches zero from the left hand side.
Once again, note that neither value can ever truly be reached.