Which of the following correctly describes the end behavior of the polynomial function, \( f(x)=-3 x^{4}+2 x^{2}-x \) ? A. The left end goes up and the right end goes down. B. Both ends go up. C. The left end goes down and the right end goes up. D. Both ends go down.

To determine the end behavior of the polynomial function \( f(x)=-3 x^{4}+2 x^{2}-x \), we focus on the leading term, which is \( -3x^4 \). Since the leading coefficient is negative and the degree (4) is even, both ends of the graph will point downwards. This means that as \( x \) approaches positive or negative infinity, \( f(x) \) will also approach negative infinity. Thus, the correct description is that both ends go down. So, the answer is D. Both ends go down.