Question

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

Explanation:

Step1: Analyze left end behavior

As \( x \to -\infty \), observe the graph's trend. The left - most part of the graph (as \( x \) becomes very small, negative infinity) is going downwards, so \( f(x)\to -\infty \) as \( x\to -\infty \).

Step2: Analyze right end behavior

As \( x \to +\infty \), observe the right - most part of the graph (as \( x \) becomes very large, positive infinity). The right - most part of the graph is going downwards, so \( f(x)\to -\infty \) as \( x\to +\infty \).

Answer:

As \( x\to -\infty \), \( f(x)\to -\infty \); as \( x\to +\infty \), \( f(x)\to -\infty \)