From the graph provided, we can identify the intervals where the function is increasing, decreasing, or constant by examining the slope between the given points.

Coordinates from the graph:

• $(-5, 2)$
• $(-3, -2)$
• $(1, 2)$
• $(4, 2)$
• $(6, -1)$

Analyzing the intervals:

1. Decreasing:

   • The graph is decreasing between $(-5, 2)$ and $(-3, -2)$, and also between $(4, 2)$ and $(6, -1)$, because the graph slopes downward between these points.
   • Interval: $(-5, -3)$ and $(4, 6)$.

2. Increasing:

   • The graph is increasing between $(-3, -2)$ and $(1, 2)$, as the graph slopes upward between these points.
   • Interval: $(-3, 1)$.

3. Constant:

   • The graph is constant between $(1, 2)$ and $(4, 2)$, since the graph forms a horizontal line segment at $y = 2$.
   • Interval: $(1, 4)$.

Final answer:

• Increasing: $(-3, 1)$
• Decreasing: $(-5, -3)$ and $(4, 6)$
• Constant: $(1, 4)$

Would you like more details or clarification on any of these intervals?

Here are 5 related questions:

1. How can you identify whether a function is increasing or decreasing on a graph?
2. What is the significance of constant intervals in a function?
3. How do critical points relate to the increasing or decreasing behavior of functions?
4. Can a function have more than one increasing or decreasing interval?
5. What is the importance of using interval notation in calculus?

Tip: When working with piecewise functions, always check for changes in slope to determine whether the function is increasing, decreasing, or constant.