$f(x)=(x+4)^{3}$ What is the equation of this function after it is reflected over the $x$-axis? A. $F(x)=-(x+4)^{3}$ B. $F(x)=y(x+4)^{3}$ C. $F(x)=-(y+4)^{3}$ D. $F(x)=(y+4)^{3}$

Step 1 ：The reflection of a function over the x-axis is achieved by changing the sign of the function. In this case, the function \(f(x)=(x+4)^{3}\) will become \(f(x)=-(x+4)^{3}\) after it is reflected over the x-axis.

Step 2 ：Therefore, the correct answer is A. \(F(x)=-(x+4)^{3}\).

Step 3 ：Final Answer: The equation of the function after it is reflected over the x-axis is \(\boxed{F(x)=-(x+4)^{3}}\).