The image you've uploaded shows a graph with labeled points and sections. To determine the intervals for positive, negative, increasing, and decreasing regions based on this graph, let’s break down the sections:

• Positive Interval: This is where the graph is above the x-axis.
• Negative Interval: This is where the graph is below the x-axis.
• Increasing Interval: This occurs when the graph moves upwards as you move from left to right.
• Decreasing Interval: This occurs when the graph moves downward as you move from left to right.

From the image:

• Positive Interval: The graph is above the x-axis for $x < -0.9$ and $x > 1.5$.
• Negative Interval: The graph is below the x-axis for $-2 < x < 1$.
• Increasing Interval: The graph is increasing between $-2 < x < -0.9$ and $0 < x < 1$.
• Decreasing Interval: The graph is decreasing between $-0.9 < x < 0$ and $1 < x < 2$.

Based on these observations, you can now match the intervals to the corresponding answers.

Let me know if you'd like more details or if you have any other questions about this!

Additional questions:

1. How do you determine the slope of a graph at a given point?
2. How would the intervals change if the graph had a horizontal line at y = 0?
3. What would happen to the intervals if the function were a sine wave?
4. Can a graph have more than one positive or negative interval? Why or why not?
5. What methods are used to find critical points in a function?

Tip: When analyzing a graph, look for turning points (local maxima or minima), as these points often mark the transition between increasing and decreasing behavior.