Question

the graph of $y = f(x)$ is graphed below. what is the end behavior of $f(x)$?
answer
attempt 1 out of 3
as $x\to -\infty,y\to -\infty$ and
as $x\to \infty,y\to -\infty$
as $x\to -\infty,y\to \infty$ and
as $x\to \infty,y\to -\infty$
as $x\to -\infty,y\to -\infty$ and
as $x\to \infty,y\to \infty$
as $x\to -\infty,y\to \infty$ and
as $x\to \infty,y\to \infty$

Explanation:

Step1: Analyze the left - hand end behavior

As \(x\) approaches \(-\infty\) (moving to the far left on the \(x\) - axis), looking at the graph, the \(y\) - values go downwards. So, as \(x\to-\infty\), \(y = f(x)\to-\infty\).

Step2: Analyze the right - hand end behavior

As \(x\) approaches \(\infty\) (moving to the far right on the \(x\) - axis), looking at the graph, the \(y\) - values go downwards. So, as \(x\to\infty\), \(y = f(x)\to-\infty\).

Answer:

As \(x\to-\infty,y\to-\infty\) and as \(x\to\infty,y\to-\infty\)