1. The function given is $$g(x) = -x^4 + 2x^3 + 5x^2 - 1$$. 2. To determine the end behavior of the polynomial, we focus on the leading term of highest degree because it dominates the function as $$x$$ approaches $$\infty$$ or $$-\infty$$. 3. The leading term here is $$-x^4$$. 4. Since the degree is 4 (which is even), the ends of the graph will go in the same direction. 5. The leading coefficient is negative ($$-1$$), so both ends of the graph will go downward. 6. Therefore, as $$x \to \infty$$, $$g(x) \to -\infty$$, and as $$x \to -\infty$$, $$g(x) \to -\infty$$. 7. This matches answer choice C. Final answer: C As $$x \to \infty$$, $$g(x) \to -\infty$$, and as $$x \to -\infty$$, $$g(x) \to -\infty$$.