From the image, you're working on identifying the intervals where the given function is increasing, decreasing, or constant. Here's how you can analyze the graph step by step:

Key Observations:

1. Increasing Interval: The function starts increasing from around $x = 2$ and continues increasing beyond $x = 3$.
2. Decreasing Interval: The function is decreasing between $x = -3$ and $x = -1$.
3. Constant Interval: The function is constant between $x = -1$ and $x = 2$.

Solutions:

1. Increasing Interval: The function is increasing on the interval $(2, \infty)$.

   • Correct choice for Part 1: "The function is sometimes increasing."
   • Interval: $(2, \infty)$.

2. Decreasing Interval: The function is decreasing on the interval $(-3, -1)$.

   • Correct choice for Part 2: "The function is sometimes decreasing."
   • Interval: $(-3, -1)$.

3. Constant Interval: The function is constant on the interval $(-1, 2)$.

   • This is the interval where the function maintains a constant value.

Would you like further details or explanation on any part of this? Here are some related questions to explore:

1. What is the significance of open intervals in describing increasing and decreasing functions?
2. How would the analysis change if the graph had closed endpoints at $x = -3$ and $x = 2$?
3. Can you describe how to find critical points from the graph?
4. How do you differentiate between strictly increasing and non-decreasing intervals on a graph?
5. How would you represent a piecewise function based on this graph?

Tip: Always pay close attention to whether the graph includes endpoints or not (open vs. closed circles) when defining intervals.