Question

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

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 upwards, so as \( x\to-\infty \), \( f(x)\to\infty \).

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 \( x\to\infty \), \( f(x)\to-\infty \).

Answer:

as \( x \to -\infty, f(x) \to \infty \) and as \( x \to \infty, f(x) \to -\infty \) (the option with this description)