Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. \( f(x)=-8 x^{3}+2 x^{2}+4 x-3 \)

To determine the end behavior of the polynomial function \( f(x)=-8 x^{3}+2 x^{2}+4 x-3 \), we focus on the leading term, which in this case is \(-8x^3\). Since the leading coefficient is negative and the degree of the polynomial (which is 3) is odd, the end behavior can be described as follows: as \( x \) approaches infinity, \( f(x) \) approaches negative infinity, and as \( x \) approaches negative infinity, \( f(x) \) approaches positive infinity. Thus, the graph will fall to the right and rise to the left. Now, when matching the function with its graph, look for the one that reflects this end behavior. Essentially, it will have a downward slope at the right side and an upward slope at the left side, clearly indicating the behavior of an odd-degree polynomial with a negative leading coefficient. Happy graph searching!