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 right end behavior

Look at the graph as \( x \to \infty \) (right end). The graph rises upwards, so \( f(x) \to \infty \).

Step2: Analyze left end behavior

Look at the graph as \( x \to -\infty \) (left end). The graph falls downwards, so \( f(x) \to -\infty \).

Answer:

as \( x \to \infty, f(x) \to \infty \) and as \( x \to -\infty, f(x) \to -\infty \) (the third option in the list)