The problem asks you to use the graph of the function to determine the intervals where the function is increasing or decreasing. Here's how you can approach this:

Step 1: Analyze the Graph

• The graph is a continuous curve with three critical points, which are the points where the slope (or derivative) changes sign.

Step 2: Identify the Critical Points

• Point 1: The curve increases until it reaches a peak at around $x = -2$.
• Point 2: The curve decreases until it reaches a trough at around $x = 0$.
• Point 3: The curve increases again after $x = 0$.

Step 3: Determine Intervals of Increase and Decrease

• Increasing Interval:
  • From $x \approx -5$ to $x \approx -2$.
  • From $x \approx 0$ to $x = 5$.
• Decreasing Interval:
  • From $x \approx -2$ to $x \approx 0$.

Step 4: Match with the Provided Choices

Based on the intervals above, the correct option should be:

• Option C: The function is increasing on $(-5, -2) \cup (0, 5)$ and decreasing on $(-2, 0)$.

Would you like more details or have any questions?

Here are some related questions that might help further your understanding:

1. What are critical points, and how are they determined from a graph?
2. How can you confirm whether a function is increasing or decreasing on a specific interval?
3. What is the significance of the first derivative in analyzing the increasing or decreasing nature of a function?
4. Can a function have more than two intervals where it is increasing or decreasing?
5. How does concavity affect the intervals of increase and decrease?

Tip: Always remember to check the endpoints of the intervals and any points where the derivative is zero to ensure you correctly identify increasing and decreasing behavior.