Question

use the graph to answer the question. describe the end behavior of the function. (1 point) $f(x)\to\infty$ as $x\to\infty$ and $f(x)\to -\infty$ as $x\to -\infty$ $f(x)\to -\infty$ as $x\to\infty$ and $f(x)\to -\infty$ as $x\to -\infty$ $f(x)\to -\infty$ as $x\to\infty$ and $f(x)\to 0$ as $x\to -\infty$ $f(x)\to\infty$ as $x\to\infty$ and $f(x)\to 0$ as $x\to -\infty$

Explanation:

Step1: Analyze the right - hand end behavior

As \(x\) approaches \(\infty\) (moving to the right along the \(x\) - axis), looking at the graph, the function values \(y = f(x)\) are decreasing without bound. So \(f(x)\to-\infty\) as \(x\to\infty\).

Step2: Analyze the left - hand end behavior

As \(x\) approaches \(-\infty\) (moving to the left along the \(x\) - axis), looking at the left - most part of the graph (the horizontal part on the left), the function values \(y = f(x)\) approach \(0\). So \(f(x)\to0\) as \(x\to-\infty\).

Answer:

\(f(x)\to-\infty\) as \(x\to\infty\) and \(f(x)\to0\) as \(x\to-\infty\) (the third option in the multiple - choice list).