To answer this question, we need to determine where the function is increasing or decreasing. Let's analyze the graph:

Step 1: Identify turning points

From the graph:

• The turning points are approximately at $x = -3$, $x = -1$, and $x = 2$. These points divide the graph into intervals.

Step 2: Analyze each interval

• Interval $(-\infty, -3)$: The function decreases as $x$ moves toward $-3$.
• Interval $(-3, -1)$: The function increases as $x$ moves from $-3$ to $-1$.
• Interval $(-1, 2)$: The function decreases as $x$ moves from $-1$ to $2$.
• Interval $(2, \infty)$: The function increases as $x$ moves away from $2$.

Step 3: Write intervals

• Increasing on: $(-3, -1) \cup (2, \infty)$
• Decreasing on: $(-\infty, -3) \cup (-1, 2)$

Final Answer:

• Increasing on the interval(s): $(-3, -1) \cup (2, \infty)$
• Decreasing on the interval(s): $(-\infty, -3) \cup (-1, 2)$

Would you like additional details on the reasoning or steps?

Here are 5 questions to deepen understanding:

1. What determines whether a function is increasing or decreasing?
2. How do turning points relate to the derivative of a function?
3. How can intervals of increase/decrease be confirmed algebraically?
4. What is the significance of local maxima and minima in determining these intervals?
5. How does concavity differ from increasing/decreasing behavior?

Tip: Use the derivative of the function to mathematically verify increasing or decreasing intervals.