From the graph provided, we need to identify the intervals where the function is increasing and decreasing.

Increasing Intervals:

The function is increasing where the slope of the curve is positive (where the curve moves upward). Based on the graph:

• The function is increasing between $x = -4$ and $x = -1$.
• The function also increases after $x = 3$, so the second interval is $(3, 5]$.

Decreasing Intervals:

The function is decreasing where the slope of the curve is negative (where the curve moves downward). Based on the graph:

• The function is decreasing between $x = -1$ and $x = 3$.

Final Answer:

• Increasing on the interval(s): $(-4, -1) \cup (3, 5]$
• Decreasing on the interval(s): $(-1, 3)$

Would you like further details on how these intervals were determined?

Here are five follow-up questions that can deepen your understanding:

1. What are critical points, and how do they relate to increasing and decreasing intervals?
2. How can the first derivative of a function help in identifying these intervals?
3. Can a function be increasing or decreasing at a single point, like at a maximum or minimum?
4. How do local maxima and minima relate to the intervals where a function increases or decreases?
5. What is the difference between increasing on an open interval and a closed interval?

Tip: Remember, a function's behavior changes at points where the derivative is zero or undefined, typically corresponding to peaks, valleys, or points of inflection.