1. Let's analyze each function and describe its graph shape based on the given information. 2. For $f(x) = -x^3 - 2x^2 - 1$, it is a cubic function with a negative leading coefficient $-1$, so as $x \to -\infty$, $f(x) \to \infty$ and as $x \to \infty$, $f(x) \to -\infty$. The graph starts high on the left near $y=10$ at $x=-10$ and goes down steeply, passing near the origin, dipping below the $x$-axis and further down near $y=-10$ at $x=10$. 3. For $g(x) = x^4 + x^3 - x^2 - 2x$, it is a quartic polynomial with a positive leading coefficient $1$. Therefore, as $x \to \pm\infty$, $g(x) \to \infty$. The graph has two upward arms on each end near $y=10$ at $x=\pm10$, dips below zero near $x=0$, and has a local minimum between $x=0$ and $x=2$. 4. For $h(x) = x^3 - 17x^2 + 93x - 168$, a cubic polynomial with positive leading coefficient. As $x \to -\infty$, $h(x) \to -\infty$, and as $x \to \infty$, $h(x) \to \infty$. The graph rises steeply from the bottom left, reaches a peak near $y=-2$ at about $x=2$, and descends steeply below $y=-10$ near $x=10$. 5. For $k(x) = -x^4 - 3x^2 - 2$, a quartic polynomial with negative leading coefficient $-1$. Therefore, as $x \to \pm\infty$, $k(x) \to -\infty$. The graph starts near $y=-10$ at $x=-10$, has complex valleys climbing above zero near $x=8$, and climbs beyond $y=10$ near $x=10$. Final key points summarize the shapes based on polynomial degree, leading coefficient, and given behavior.