Question

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

Explanation:

Step1: Analyze left end behavior

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

Step2: Analyze right end behavior

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

Answer:

as \( x \to -\infty \), \( f(x) \to -\infty \) and as \( x \to \infty \), \( f(x) \to -\infty \) (the first option: "as \( x \to -\infty, f(x) \to -\infty \) and as \( x \to \infty, f(x) \to -\infty \)")