Question

refer to the graph of y = f(x) to the right to describe the behavior of lim f(x) as x→∞. use -∞ and ∞ where appropriate. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)=□ as x→∞ b. the limit does not exist and is neither -∞ nor ∞.

Explanation:

Step1: Analyze the graph as x approaches infinity

As \(x\to\infty\), observe the long - term behavior of the function \(y = f(x)\) from the graph. The function appears to approach a horizontal asymptote.

Step2: Determine the limit value

By looking at the right - hand side of the graph as \(x\) gets larger and larger, we can see that the function values are approaching a specific value. In this case, as \(x\to\infty\), the function \(y = f(x)\) approaches a horizontal line \(y=- 2\). So \(\lim_{x\to\infty}f(x)=-2\).

Answer:

A. \(\lim_{x\to\infty}f(x)= - 2\)