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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?

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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.

Use the graph of this function to estimate the intervals on which the function is increasing or decreasing.

This problem involves using a graph to determine the intervals where a function is increasing or decreasing. Key concepts include understanding the first derivative test and analyzing critical points. Suitable for students in Grades 10-12.

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