To determine the intervals on which the function is increasing, decreasing, or constant, we need to analyze the graph provided.

From the graph:

• The function increases where the curve is going up as we move from left to right.
• The function decreases where the curve is going down as we move from left to right.
• The function is constant where the graph is a horizontal line.

Intervals where the function is increasing:

By inspecting the graph, the function is increasing between $x = -4$ and $x = 1$, and then it continues increasing after $x = 6$ onward.

Therefore, the increasing intervals are:

$(-4, 1) \cup (6, \infty)$

Do you need any further details on these intervals, or would you like to proceed with the decreasing and constant intervals?

Follow-up questions:

1. How do you identify the intervals on which a function is decreasing?
2. What happens to the behavior of a function if it has a horizontal tangent?
3. Can you describe how to find local minima and maxima from a graph?
4. What does it mean for a function to be constant on an interval?
5. How would you graph a piecewise function showing increasing, decreasing, and constant segments?

Tip:

When analyzing graphs for increasing or decreasing behavior, look for the slope of the curve: an upward slope means increasing, and a downward slope means decreasing.