Step 1 :Determine whether the equation defines $y$ as a function of $x$ for the equation $x=y^{2}$.
Step 2 :In order for an equation to define y as a function of x, each x value must correspond to exactly one y value.
Step 3 :In the given equation, $x=y^{2}$, for each positive x value, there are two corresponding y values (one positive and one negative).
Step 4 :Therefore, the equation does not define y as a function of x.
Step 5 :\(\boxed{\text{No, the equation does not define } y \text{ as a function of } x}\)