1. The problem asks to determine the intervals where the function $f(x)$ is decreasing given the graph of its derivative $f'(x)$. 2. Important rule: A function $f(x)$ is decreasing where its derivative $f'(x)$ is less than zero, i.e., $f'(x) < 0$. 3. From the graph description, $f'(x)$ crosses the x-axis at approximately $x = -1.3$, $x = -0.5$, and $x = 2.8$. 4. The graph of $f'(x)$ is below the x-axis (negative) between $-0.5$ and $2.8$. 5. Therefore, $f(x)$ is decreasing on the interval $$(-0.5, 2.8)$$. 6. Checking the options given: - ▲ $(-1.3, -0.5) \cup (0.5, 2.8)$ includes part of the negative region but incorrectly splits it. - ♦ $((-2, -1.3) \cup (-0.5, 0.5) \cup (2.8, 3))$ includes intervals where $f'(x)$ is positive. - ● $(-2, -1) \cup (0, 2)$ partially overlaps but includes positive derivative intervals. - ■ $(-1, 0) \cup (2, 3)$ also includes positive derivative intervals. 7. The correct interval where $f'(x) < 0$ and thus $f(x)$ is decreasing is $$(-0.5, 2.8)$$. Final answer: $f(x)$ is decreasing on the interval $$(-0.5, 2.8)$$.