Question

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

Explanation:

Step1: Analyze left end behavior

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

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \) (right direction). The right - most part of the graph is going upwards, 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 choices)