For the polynomial function $f(x)=-3 x^{4}+6 x^{3}$, answer the parts a through e.
a. Use the Leading Coefficient Test to determine the graph's end behavior.
A. The graph of $f(x)$ rises to the left and falls to the right.
B. The graph of $f(x)$ rises to the left and rises to the right.
C. The graph of $f(x)$ falls to the left and rises to the right.
D. The graph of $f(x)$ falls to the left and falls to the right.

Step 1 ：The Leading Coefficient Test states that the end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient. In this case, the degree of the polynomial is 4, which is even, and the leading coefficient is -3, which is negative. For polynomial functions with an even degree, the ends of the graph will point in the same direction. If the leading coefficient is positive, the graph will rise to the left and right. If the leading coefficient is negative, the graph will fall to the left and right. Therefore, the graph of this function falls to the left and falls to the right.

Step 2 ：Final Answer: \(\boxed{\text{D. The graph of } f(x) \text{ falls to the left and falls to the right.}}\)