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).