Question

refer to the graph of y = f(x) to the right to describe the behavior of lim f(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: Analyze the graph as x→∞

As \(x\) approaches positive infinity, we observe the end - behavior of the graph of \(y = f(x)\). Looking at the right - hand side of the graph, we see that the function values are approaching a horizontal asymptote.

Step2: Determine the limit value

By visually inspecting the graph, as \(x\) gets larger and larger (tends to \(\infty\)), the \(y\) - values of the function \(y = f(x)\) approach \(0\).

Answer:

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