describe the end behavior (long run behavior) of f(x)=-x^2 as x→-∞, f(x)→? as x→∞, f(x)→? question help: video

Explanation:

Step1: Analyze when $x\to-\infty$

Let $x$ be a very large - negative number. Then $x^{2}$ is a very large positive number since a negative number squared is positive. And $f(x)=-x^{2}$, so as $x\to-\infty$, $f(x)\to-\infty$.

Step2: Analyze when $x\to\infty$

Let $x$ be a very large positive number. Then $x^{2}$ is a very large positive number. Since $f(x)=-x^{2}$, as $x\to\infty$, $f(x)\to-\infty$.

Answer:

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