Let's analyze the graph to determine where the function is increasing, decreasing, or constant. The graph provided shows a piecewise linear function with distinct segments. Here's how we can break down each part:

Increasing:

• A function is increasing where its slope is positive (moving upwards from left to right).
• Looking at the graph, the function is increasing from $x = -6$ to $x = -2$, and again from $x = 3$ to $x = 6$.

Therefore, the function is increasing on the intervals:

• $(-6, -2)$
• $(3, 6)$

Decreasing:

• A function is decreasing where its slope is negative (moving downwards from left to right).
• On the graph, the function is decreasing from $x = -2$ to $x = 3$.

Therefore, the function is decreasing on the interval:

• $(-2, 3)$

Constant:

• A function is constant where the graph is flat (no change in $y$-value as $x$ changes).
• In the given graph, the function is constant from $x = 6$ to $x = 7$.

Therefore, the function is constant on the interval:

• $(6, 7)$

Final Answers:

• (a) Increasing: $(-6, -2)$, $(3, 6)$
• (b) Decreasing: $(-2, 3)$
• (c) Constant: $(6, 7)$

Do you have any questions or would you like more details?

Here are 5 related questions you can explore:

1. What is the difference between open and closed intervals in calculus?
2. How can you determine if a function is increasing or decreasing using derivatives?
3. How do piecewise functions behave differently from continuous functions?
4. How do you interpret slope and concavity in a function's graph?
5. What are the implications of a function being constant over an interval?

Tip: When identifying increasing or decreasing intervals, look at the behavior of the graph's slope between specific points.