Which rule should be applied to reflect $f(x)=x^{3}$ over the $x$ axis? A. Multiply $f(x)$ by -1 B. Switch the variables $x$ and $y$ in the equation C. Multiply $f(y)$ by -1 D. Substitute $-x$ for $x$ and simplify $f(-x)$

Step 1 ：The problem is asking for the rule to reflect the function $f(x)=x^{3}$ over the $x$ axis.

Step 2 ：To reflect a function over the x-axis, we need to change the sign of the y-values. In the context of a function, this means we need to multiply the function by -1.

Step 3 ：Therefore, the correct answer should be A. Multiply $f(x)$ by -1.

Step 4 ：Final Answer: \(\boxed{\text{A. Multiply } f(x) \text{ by -1}}\)