Question

use the graph to answer the question. describe the end behavior of the graphed function. (1 point) $f(x)\to2$ as $x\to-\infty$ and $f(x)\to\infty$ as $x\to\infty$ $f(x)\to-\infty$ as $x\to2$ and $f(x)\to\infty$ as $x\to\infty$ $f(x)\to2$ as $x\to-\infty$ and $f(x)\to\infty$ as $x\to4$ $f(x)\to-\infty$ as $x\to-\infty$ and $f(x)\to\infty$ as $x\to\infty$

Explanation:

Step1: Analyze the left - hand end behavior

As \(x\to-\infty\), we observe the graph. The \(y\) - values of the function approach a horizontal line \(y = 2\). So, \(f(x)\to2\) as \(x\to-\infty\).

Step2: Analyze the right - hand end behavior

As \(x\to+\infty\), we look at the graph. The \(y\) - values of the function keep increasing without bound. So, \(f(x)\to+\infty\) as \(x\to+\infty\).

Answer:

\(f(x)\to2\) as \(x\to-\infty\) and \(f(x)\to\infty\) as \(x\to\infty\)