Question

the graph of $y = f(x)$ is graphed below. what is the end behavior of $f(x)$?

answer

• as $x \to \infty, f(x) \to -\infty$ and as $x \to -\infty, f(x) \to -\infty$
• as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to \infty$
• as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to -\infty$
• as $x \to \infty, f(x) \to -\infty$ and as $x \to -\infty, f(x) \to \infty$

Explanation:

Step1: Analyze right end behavior

As \( x \to +\infty \), observe the graph's right - most part. The graph is rising upwards, so \( f(x)\to+\infty \) as \( x \to +\infty \).

Step2: Analyze left end behavior

As \( x \to -\infty \), observe the graph's left - most part. The graph is falling downwards, so \( f(x)\to-\infty \) as \( x \to -\infty \).

Answer:

As \( x \to \infty \), \( f(x) \to \infty \) and as \( x \to -\infty \), \( f(x) \to -\infty \) (the corresponding option among the given choices which has this description)