Let's analyze the graph in the image to determine the intervals where the function $f(x)$ is increasing, decreasing, and constant.

Constant Intervals:

• From $x = -10$ to $x = -2$, the function appears constant at $f(x) = -2$.
• From $x = 1$ to $x = 3$, the function appears constant at $f(x) = 3$.

Increasing Intervals:

• From $x = 3$ to $x = 5$, the function is decreasing (as it heads downward) until it reaches a minimum.
• From $x = 5$ to $x = 10$, the function is increasing.

Decreasing Intervals:

• From $x = -2$ to $x = 1$, the function increases from a value near $-2$ to 3.

Thus, the intervals where the function is increasing, decreasing, and constant are:

• Constant: $(-10, -2] \cup [1, 3]$
• Increasing: $(5, 10]$
• Decreasing: $(3, 5]$

Would you like a detailed explanation of any part of this, or do you have any questions?

Related questions:

1. How do we find critical points in a function?
2. What are the differences between local and global maxima/minima?
3. How do we compute intervals of concavity for a function?
4. Can we determine whether the function is differentiable at the constant intervals?
5. How can first derivative tests help confirm increasing or decreasing behavior?

Tip: Always examine the behavior of the function at endpoints when dealing with intervals, as it can affect whether they are included in the increasing or decreasing set.