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

Explanation:

Step1: Recall derivative - slope relationship

The derivative $f'(x)$ represents the slope of the tangent line to the graph of $y = f(x)$.

Step2: Analyze left - hand end behavior

As $x\to-\infty$, the graph of $y = f(x)$ is increasing first and then decreasing. So, $f'(x)$ is positive initially and then negative as $x\to-\infty$.

Step3: Analyze right - hand end behavior

As $x\to+\infty$, the graph of $y = f(x)$ is decreasing. So, $f'(x)<0$ as $x\to+\infty$.

Answer:

As $x\to-\infty$, $f'(x)$ changes sign (from positive to negative); as $x\to+\infty$, $f'(x)<0$.