For the polynomial function $$ f(x)=-4 x^{4}+8 x^{3} $$, answer the parts a through e. A. The graph of $$ f(x) $$ falls 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 $$ f(x) $$ rises to the left and falls to the right. D. The graph of $$ f(x) $$ falls to the left and rises to the right.

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1. Identify the leading term of the function:  
   $$
   f(x) = -4x^4 + 8x^3
   $$
   The leading term is $$-4x^4$$.

2. Determine the degree and the sign of the leading coefficient:  
   - The degree is $$4$$ (an even number).  
   - The leading coefficient is $$-4$$ (a negative number).

3. Recall the end behavior for even-degree polynomials:  
   - If the leading coefficient is positive, the graph rises to both the left and right.  
   - If the leading coefficient is negative, the graph falls to both the left and right.

4. Apply these rules to the given function:  
   Since the degree is even and the coefficient is negative, the graph of $$f(x)$$ falls to the left and falls to the right.

Thus, the correct answer is option A.
The graph of $$ f(x) $$ falls to the left and falls to the right.

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