To analyze the graph and answer the questions, let's break it down:

a. Open intervals where the function is increasing:

From the graph, the function appears to be decreasing from left to right. There is no section where the graph is rising as you move along the x-axis. Therefore:

• There are no intervals where the function is increasing.

b. Open intervals where the function is decreasing:

Looking at the graph, the function decreases from $(-2, 7)$ to around $(3, 2)$. This is the only section where the graph slopes downward.

• The function is decreasing on the interval $(-2, 3)$.

c. Open intervals where the function is constant:

From the point $(3, 2)$ onwards, the graph is a straight horizontal line, indicating the function is constant. Therefore, the function remains constant after $x = 3$.

• The function is constant on the interval $(3, \infty)$.

Summary:

• a. Increasing intervals: None
• b. Decreasing intervals: $(-2, 3)$
• c. Constant intervals: $(3, \infty)$

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

1. What would change if the graph had a positive slope at any interval?
2. Can you express the piecewise function for the given graph?
3. How do you find the average rate of change on a given interval?
4. What are the real-life scenarios where functions increase, decrease, and remain constant?
5. How would you define the derivative at different points of this graph?

Tip: The behavior of a function (increasing, decreasing, or constant) can often be determined from its derivative. A positive derivative indicates an increasing function, while a negative derivative indicates a decreasing function. A zero derivative suggests the function is constant on that interval.