1. The problem involves matching each polynomial function to its described graph characteristics. 2. For $f(x) = -x^3 - 2x^2 - 1$: - This is a cubic polynomial with a leading coefficient negative, so it generally decreases to the right. - Description states it goes from near $y=10$ at $x\approx -3$ down to about $y=-10$ near $x=2$, matching a cubic shape with a downward trend. - Matches: Top-left graph. 3. For $g(x) = x^4 + x^3 - x^2 - 2x$: - Quartic polynomial (degree 4), tends to have a W- or M-shape. - Symmetry around y-axis is unusual due to odd power terms, but described as quartic with turning points near y-axis and passing through near 0 at $x=1$. - Matches: Top-right graph. 4. For $h(x) = x^3 - 17x^2 + 93x - 168$: - Cubic polynomial with roots near $x=3,7,8$. - The graph shows local minima and maxima between those points. - Matches: Bottom-left graph. 5. For $k(x) = -x^4 - 3x^2 - 2$: - Quartic polynomial with negative leading coefficient, opens downward. - Has a local minimum near $x=0$ and quickly declines for large $|x|$. - Matches: Bottom-right graph. Final matching results: - $f(x)$ : top-left - $g(x)$ : top-right - $h(x)$ : bottom-left - $k(x)$ : bottom-right