As x → ∞ and x → -∞, what happens to f(x) = -3x^4 + 2x² - 1?

The end behavior of a polynomial is determined by its leading term, here $-3x^4$. The degree $4$ is even, so both ends point in the same direction. The leading coefficient $-3$ is negative, so both ends point down: $f(x)\to-\infty$ as $x\to\infty$ and as $x\to-\infty$, choice J. For example, $f(10)=-30{,}000+200-1$ is very negative, and $f(-10)$ gives the same value. Choice F would need a positive leading coefficient. Choices G and H describe odd-degree behavior, where the ends point in opposite directions.