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)=□ (x→∞) b. the limit does not exist and is neither -∞ nor ∞.

Explanation:

Step1: Observe the graph as x approaches infinity

As \(x\to\infty\), we look at the right - hand end behavior of the graph of \(y = f(x)\).

Step2: Determine the limit value

By observing the graph, we can see that as \(x\) gets larger and larger (tends to infinity), the function values approach a certain horizontal line. If the graph levels off to a single value \(L\) as \(x\to\infty\), then \(\lim_{x\to\infty}f(x)=L\). If it does not level off to a single value and does not go to \(\pm\infty\), the limit does not exist and is neither \(-\infty\) nor \(\infty\). In this case, by looking at the graph, as \(x\to\infty\), the function values seem to approach a horizontal asymptote. Let's assume from the graph that the function approaches a value \(y = 0\) as \(x\to\infty\) (since the graph appears to flatten out towards \(y = 0\) as \(x\) moves to the right). So \(\lim_{x\to\infty}f(x)=0\).

Answer:

A. \(\lim_{x\to\infty}f(x)=0\)