1. The problem asks for the end behavior of the polynomial function $$f(x) = -7x^6 - 63x^5 - 77x^4 + 343x^3 + 168x^2 - 700x + 336$$. 2. To determine end behavior, focus on the term with the highest degree because it dominates the function as $$x \to \pm \infty$$. 3. The highest degree term is $$-7x^6$$. Since the degree 6 is even and the leading coefficient is negative (-7), the end behavior is: - As $$x \to \infty$$, $$f(x) \to -\infty$$ - As $$x \to -\infty$$, $$f(x) \to -\infty$$ 4. This means the graph falls to negative infinity on both ends. 5. Comparing with the options: - Option a: as $$x \to \infty$$, $$y \to -\infty$$ and as $$x \to -\infty$$, $$y \to -\infty$$ matches our conclusion. Final answer: Option a.