1. **Stating the problem:** We are given a cubic polynomial function of degree 3 with a negative leading coefficient, described by the graph in vi: a cubic graph with inflection points, descending from top left, crossing the x-axis near 0, and descending sharply. 2. **General form and properties:** A cubic polynomial can be written as $$f(x) = ax^3 + bx^2 + cx + d$$ where $a \neq 0$. Since the leading coefficient is negative, $a < 0$. 3. **Interpreting the graph description:** - The graph descends from the top left, so as $x \to -\infty$, $f(x) \to \infty$ if $a$ were positive, but since $a$ is negative, it goes to $-\infty$. - It crosses the x-axis near 0, so $f(0) = d$ is near 0. - It descends sharply after crossing the x-axis, consistent with a negative leading coefficient. 4. **Example function:** A simple cubic with negative leading coefficient and root at 0 is $$f(x) = -x^3$$. 5. **Verification:** - Leading coefficient $a = -1 < 0$. - Crosses x-axis at $x=0$. - Descends from top left to bottom right. 6. **Final answer:** The polynomial function is $$f(x) = -x^3$$.