Question

given the following graph of a function f(x), determine \\(\lim\limits_{x \to \infty} f(x)\\). (if an answer does not exist, enter dne.)

Explanation:

Step1: Analyze the right - hand end of the graph

As \(x\) approaches \(+\infty\), we look at the behavior of the function \(y = f(x)\) on the far - right side of the \(x\) - axis. From the given graph, we can see that as \(x\) gets larger and larger (moves towards \(+\infty\)), the \(y\) - value of the function approaches a horizontal line.

Step2: Determine the limit value

The horizontal line that the function approaches as \(x
ightarrow+\infty\) has a \(y\) - value of \(2\). By the definition of the limit as \(x\) approaches infinity, if the function \(f(x)\) approaches a constant \(L\) as \(x\) becomes arbitrarily large, then \(\lim_{x
ightarrow+\infty}f(x)=L\). In this case, as \(x
ightarrow+\infty\), \(f(x)\) approaches \(2\).

Answer:

\(2\)