To determine where the function is increasing, decreasing, or constant, we can analyze the graph provided in the image:

Steps to Analyze the Graph:

• Increasing: The function increases when the slope of the graph is positive (i.e., the function moves upwards from left to right).
• Decreasing: The function decreases when the slope of the graph is negative (i.e., the function moves downwards from left to right).
• Constant: The function is constant when the graph is a horizontal line (i.e., there is no change in $y$-value over an interval of $x$).

Detailed Breakdown:

1. Increasing Intervals:

   • From $x = -5$ to $x = -3$: The graph rises.
   • From $x = 3$ to $x = 6$: The graph rises again.

2. Decreasing Interval:

   • From $x = -3$ to $x = -1$: The graph drops sharply.

3. Constant Intervals:

   • From $x = -1$ to $x = 2$: The graph remains flat.

Answers in Interval Notation:

(a) The function is increasing on the intervals: $(-5, -3) \cup (3, 6)$.

(b) The function is decreasing on the interval: $(-3, -1)$.

(c) The function is constant on the interval: $(-1, 2)$.

Let me know if you'd like further details or clarifications.

Follow-up Questions:

1. What are some other common types of behavior a function can have besides increasing, decreasing, and constant?
2. How can you tell if a function is continuous from its graph?
3. How do intervals of increase and decrease relate to the derivative of the function?
4. How would the graph look if the function had a local maximum or minimum?
5. Can a function have overlapping increasing and decreasing intervals?

Tip:

When working with intervals, always remember to use open intervals (parentheses) when endpoints aren't included in the behavior, and closed intervals (brackets) when endpoints are included.