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 \( x \to -\infty \) (moving left on the x - axis). 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 \( x \to \infty \) (moving right on the x - axis). 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 last option in the list of answer choices)