Let's analyze each part of the question using the graph provided:

1. Increasing Intervals (a): The function is increasing where the curve moves upward as we move from left to right.

   • From $x = -\infty$ to $x = 2$.
   • From $x = 1$ to $x = 4$.

   Therefore, the function is increasing on the intervals $(-\infty, 2)$ and $(1, 4)$.

2. Decreasing Intervals (b): The function is decreasing where the curve moves downward as we move from left to right.

   • From $x = 2$ to $x = 3$.
   • From $x = 4$ to $\infty$.

   So, the function is decreasing on the intervals $(2, 3)$ and $(4, \infty)$.

3. Constant Intervals (c): The function is constant where the curve is flat (horizontal) and does not increase or decrease. From observing the graph, there are no intervals where the function is flat.

   Therefore, there are no constant intervals for this function.

The correct answer for each part is as follows:

• (a) Increasing intervals: $(-\infty, 2)$ and $(1, 4)$.
• (b) Decreasing intervals: $(2, 3)$ and $(4, \infty)$.
• (c) No constant intervals.

Would you like further details on any part of this explanation?

Here are 5 questions to expand on this information:

1. What is the difference between open and closed intervals in terms of graphing?
2. How can you determine increasing and decreasing intervals for functions without a graph?
3. What is the role of critical points in finding intervals of increase and decrease?
4. Can functions have overlapping increasing and decreasing intervals? Why or why not?
5. How would adding a constant to this function affect its intervals of increase and decrease?

Tip: Remember that endpoints in open intervals (like $2$ in $(-\infty, 2)$) are not included, which means the behavior of the function at exactly $x = 2$ is not considered in that interval.