9 describe the end behavior of the function. f(x)=-x^4 + x^2 - 2 f(x)→∞ f(x)→-∞ as x→∞ ○ ○ as x→-∞ ○ ○

Explanation:

Step1: Identify the leading - term

The leading - term of the polynomial function $f(x)=-x^{4}+x^{2}-2$ is $-x^{4}$. The degree $n = 4$ (even) and the leading - coefficient $a=-1$ (negative).

Step2: Analyze as $x\to\infty$

For a polynomial function $y = a_nx^n+\cdots+a_0$, when $n$ is even and $a_n<0$, as $x\to\infty$, we consider the behavior of the leading - term. Since $y=-x^{4}$ and $x\to\infty$, then $y = -x^{4}\to-\infty$. So $f(x)\to-\infty$ as $x\to\infty$.

Step3: Analyze as $x\to-\infty$

When $n$ is even, $(-x)^n=x^n$. For the leading - term $y = -x^{4}$, when $x\to-\infty$, we have $y=-(-x)^{4}=-x^{4}\to-\infty$. So $f(x)\to-\infty$ as $x\to-\infty$.

Answer:

As $x\to\infty$, $f(x)\to-\infty$; As $x\to-\infty$, $f(x)\to-\infty$