Question

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

Explanation:

Step1: Analyze left end behavior

Look at the graph as \( x \to -\infty \) (left side). The left - most part of the graph is going downwards, so as \( x \to -\infty \), \( y \to -\infty \).

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \) (right side). The right - most part of the graph is going downwards, so as \( x \to \infty \), \( y \to -\infty \).

Answer:

as \( x \to -\infty,y \to -\infty \) and as \( x \to \infty,y \to -\infty \) (the third option in the list of answer choices)