What is the end behavior of $f(x)=-3 x^{2}+4 x-1$ ? A. as $x \rightarrow \infty, f(x) \rightarrow \infty$ as $x \rightarrow-\infty, f(x) \rightarrow-\infty$ B. as $x \rightarrow \infty, f(x) \rightarrow \infty$ as $x \rightarrow-\infty, f(x) \rightarrow \infty$ C. as $x \rightarrow \infty, f(x) \rightarrow-\infty$ as $x \rightarrow-\infty, f(x) \rightarrow-\infty$ D. as $x \rightarrow \infty, f(x) \rightarrow-\infty$ as $x \rightarrow-\infty, f(x) \rightarrow \infty$

Step 1 ：The function given is \(f(x)=-3 x^{2}+4 x-1\).

Step 2 ：The end behavior of a function is determined by the degree and the leading coefficient of the polynomial.

Step 3 ：In this case, the degree of the polynomial is 2 (even) and the leading coefficient is -3 (negative).

Step 4 ：For even-degree polynomials, both ends of the graph will point in the same direction. If the leading coefficient is positive, both ends will point upwards, and if it is negative, both ends will point downwards.

Step 5 ：So, as x approaches infinity, the value of f(x) should approach negative infinity. Similarly, as x approaches negative infinity, the value of f(x) should also approach negative infinity.

Step 6 ：Final Answer: The end behavior of the function \(f(x)=-3 x^{2}+4 x-1\) is as \(x \rightarrow \infty, f(x) \rightarrow-\infty\) and as \(x \rightarrow-\infty, f(x) \rightarrow-\infty\). So, the correct answer is \(\boxed{\text{C}}\).