1. We are given four functions $f(x)$, $g(x)$, $h(x)$, and $k(x)$ with their polynomial expressions. 2. Let's analyze each function's general shape based on degree and leading coefficient. 3. Function $f(x) = -x^3 - 21x^2 - 144x - 325$ is a cubic polynomial with leading coefficient $-1$. 4. Since the leading coefficient is negative and the degree is odd (3), its graph will rise to the left and fall to the right, making a downward curve overall. 5. Function $g(x) = 2x^4 + 4x^3 + 4x^2 + 4x + 2$ is a quartic polynomial with positive leading coefficient $2$. 6. For quartics with positive leading coefficients, the end behavior is upwards on both sides, generally creating a U-shaped or W-shaped graph. The given expression suggests a U-shaped curve near origin due to dominant $2x^4$ term. 7. Function $h(x) = 2x^3 + 6x^2$ is cubic with positive leading coefficient $2$. 8. Positive leading odd-degree polynomials typically have an S-shaped curve, rising from bottom-left to top-right. 9. Function $k(x) = -x^4 - 4x^2 + x - 3$ is a quartic with negative leading coefficient $-1$. 10. Negative quartic leading coefficient means the graph generally opens downward, resembling an inverted U shape. 11. Summary: - Bottom-left graph: $f(x)$, cubic, negative leading coefficient, downwards curve. - Top-right graph: $g(x)$, quartic, positive leading, upwards U-shape. - Bottom-right graph: $h(x)$, cubic, positive leading, S-shaped curve. - Top-left graph: $k(x)$, quartic, negative leading, inverted U shape. This matches the given descriptions and confirms the shapes.