find the limits of f at negative and positive infinity. lim f(x) = x→−∞ lim f(x) = x→∞

Explanation:

Step1: Analyze limit as $x\to-\infty$

As $x$ approaches negative infinity, looking at the graph, the function $f(x)$ approaches $0$. So $\lim_{x\to-\infty}f(x)=0$.

Step2: Analyze limit as $x\to\infty$

As $x$ approaches positive infinity, from the graph, the function $f(x)$ approaches $0$. So $\lim_{x\to\infty}f(x)=0$.

Answer:

$\lim_{x\to-\infty}f(x)=0$ $\lim_{x\to\infty}f(x)=0$