Question

use the graph of the rational function to complete the following statement. as x → ∞, f(x) → ____. as x → ∞, f(x) →\boxed{}.

Explanation:

Step1: Analyze the right - hand end of the graph

We need to determine the behavior of the function \(f(x)\) as \(x\) approaches positive infinity (\(x
ightarrow\infty\)). To do this, we look at the part of the graph where \(x\) is very large (far to the right on the \(x\) - axis).

Step2: Observe the trend of the graph as \(x

ightarrow\infty\)
From the given graph of the rational function, when we look at the right - most part of the graph (as \(x\) gets larger and larger, moving towards positive infinity), we can see that the graph of the function is approaching \(y = 0\) (the \(x\) - axis) from below? Wait, no, let's re - examine. Wait, the right - hand part of the graph (for large positive \(x\)): looking at the graph, as \(x\) approaches positive infinity, the curve is approaching \(y = 0\) from above? Wait, no, the graph on the right (for \(x>4\) or so) shows that as \(x\) gets very large (goes to \(\infty\)), the \(y\) - value of the function approaches \(0\) from below? Wait, no, let's check the graph again. The right - hand branch of the rational function (the one on the right side of the vertical asymptote) is approaching the \(x\) - axis ( \(y = 0\)) as \(x\) approaches \(\infty\). So as \(x
ightarrow\infty\), \(f(x)\) approaches \(0\).

Answer:

\(0\)