Graph the following function.
\[
f(x)=-\frac{1}{7} x^{2}
\]
Determine the transformation(s) that need to be applied to $g(x)=x^{2}$ to obtain the graph of $f(x)=-\frac{1}{7} x^{2}$
Select all that apply.
A. Vertical stretch or shrink.
B. Horizontal stretch or shrink.
C. Reflect across $y$-axis.
D. Reflect across $\mathrm{x}$-axis.
E. Vertical translation up
F. Horizontal translation to the right.
G. Horizontal translation to the left.
H. Vertical translation down.

Step 1 ：The function \(f(x)=-\frac{1}{7} x^{2}\) is a transformation of the function \(g(x)=x^{2}\).

Step 2 ：The negative sign in front of the fraction indicates a reflection across the x-axis.

Step 3 ：The fraction \(\frac{1}{7}\) indicates a vertical shrink by a factor of \(\frac{1}{7}\).

Step 4 ：There is no addition or subtraction inside or outside the function, so there are no horizontal or vertical translations.

Step 5 ：There is also no multiplication or division by a constant inside the function, so there is no horizontal stretch or shrink.

Step 6 ：Therefore, the transformations that need to be applied to \(g(x)=x^{2}\) to obtain the graph of \(f(x)=-\frac{1}{7} x^{2}\) are a reflection across the x-axis and a vertical shrink by a factor of \(\frac{1}{7}\).

Step 7 ：\(\boxed{\text{A, D}}\)