Let's analyze the graph to determine the intervals where the function is increasing, decreasing, and constant.

Key observations:

• Increasing intervals: These are portions where the graph is moving upwards as you go from left to right.
• Decreasing intervals: These are portions where the graph moves downwards as you go from left to right.
• Constant intervals: These are portions where the graph is flat, meaning no change in the $y$-value as $x$-increases.

From the graph:

1. Constant interval:

   • From $x = -9$ to $x = -6$, the function is constant. The graph is a horizontal line in this region.

2. Decreasing interval:

   • From $x = -6$ to $x = 1$, the function is decreasing, as the graph is sloping downwards.

3. Increasing intervals:

   • From $x = 1$ to $x = 6$, the graph is sloping upwards, meaning the function is increasing.
   • From $x = 6$ to $x = 8$, the function is again increasing after a dip.

Answers:

• The correct intervals where the function is increasing are: $(-6, 1)$ and $(6, 8)$. This corresponds to option C.

• The interval where the function is decreasing is: $(-6, 1)$, which is what the question asks second.

Would you like more detailed steps or explanations on how we identify increasing, decreasing, and constant functions?

Related questions:

1. How can you determine the concavity of a function from a graph?
2. How does the behavior of a function change at critical points?
3. What are the characteristics of a function that is strictly increasing?
4. How can piecewise functions be analyzed for continuity?
5. What are the common types of functions that have intervals of increase and decrease?

Tip: Remember, the slope of a function tells you whether it's increasing (positive slope) or decreasing (negative slope).