https://file.aiquickdraw.com/mathbot/file/1725495873004yylxxszq.jpg

To solve the problem, we'll analyze the graph provided.

### Step 1: Determine where the function is **increasing**.
A function is increasing on an interval if, as \( x \) moves from left to right, the function's values (i.e., \( y \)-values) are increasing. This happens when the graph is sloping upwards.

From the graph:
- The function increases from \( x = -6 \) to \( x = -2 \).
- The function also increases from \( x = 2 \) to \( x = 4 \).

Thus, the intervals where the function is increasing are \( (-6, -2) \) and \( (2, 4) \).

### Step 2: Determine where the function is **decreasing**.
A function is decreasing on an interval if, as \( x \) moves from left to right, the function's values are decreasing. This happens when the graph is sloping downwards.

From the graph:
- The function decreases from \( x = -2 \) to \( x = 2 \).
- The function also decreases from \( x = 4 \) to \( x = 6 \).

Thus, the intervals where the function is decreasing are \( (-2, 2) \) and \( (4, 6) \).

### Final Answers:
1. **For increasing intervals (Part A):** The answer is \( (-6, -2) \) and \( (2, 4) \).
2. **For decreasing intervals (Part B):** The answer is \( (-2, 2) \) and \( (4, 6) \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. What is the significance of a critical point in determining increasing or decreasing intervals?
2. How does the derivative of a function relate to its increasing or decreasing behavior?
3. Can a function be increasing or decreasing on an open interval?
4. How would you describe a function that is neither increasing nor decreasing on an interval?
5. How do you find the maximum and minimum points on the graph of a function?

**Tip:** When analyzing a graph for increasing and decreasing intervals, always check the slopes and note where they change sign (from positive to negative or vice versa).

Use the graph of f to determine intervals where f is increasing and where f is decreasing.

Learn how to determine where a function is increasing or decreasing by analyzing its graph. This problem involves interpreting the graph of a function and applying key calculus concepts, such as the first derivative test and monotonicity. Suitable for high school students in Grades 10-12.

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