Answer:
The correct option is C.
Step-by-step explanation:
The given function is
![F(x)=x^2](https://tex.z-dn.net/?f=F%28x%29%3Dx%5E2)
The transformation of the function is defined as
![G(x)=kF(x)](https://tex.z-dn.net/?f=G%28x%29%3DkF%28x%29)
If k>1, then the graph of function F(x) stretched vertically and If 0<k<1, then the graph of function F(x) compressed vertically.
It is given that the graph of F(x) can be stretched vertically, it means the value of k must be greater than 1.
The graph of F(x) is flipped over the x-axis, so the function G(x) is equal to the negative of k times of F(x).
![G(x)=-kF(x)](https://tex.z-dn.net/?f=G%28x%29%3D-kF%28x%29)
Where must be greater than 1.
In option 3, G(x) is equal to the negative of 4 times of F(x). Only in this option, there is negative relation between F(x) and g(x) with k>1.
![G(x)=-4F(x)](https://tex.z-dn.net/?f=G%28x%29%3D-4F%28x%29)
Therefore the correct option is C.