Looking at the graph provided, the function is a smooth curve that resembles a polynomial of degree 3. We can determine the intervals where the function is increasing and decreasing by analyzing the slopes of the graph.

Steps to identify:

• The function is increasing where the slope of the curve is positive (moving upwards).
• The function is decreasing where the slope of the curve is negative (moving downwards).

From the graph:

1. The function starts by decreasing from $x = -\infty$ until it reaches its first local minimum at approximately $x = -7$.
2. It then increases from $x = -7$ to its local maximum at $x = -1$.
3. From $x = -1$, it decreases until it reaches a local minimum at $x = 5$.
4. After $x = 5$, the function begins to increase again as it heads towards $x = \infty$.

Answer:

• Increasing intervals: The function is increasing on the intervals $(-7, -1) \cup (5, \infty)$.
• Decreasing intervals: The function is decreasing on the intervals $(-\infty, -7) \cup (-1, 5)$.

Would you like further clarification or details on this solution?

Here are 5 related questions to expand understanding:

1. How do we identify local maxima and minima using a graph?
2. What is the difference between local and global extrema?
3. Can the derivative of a function help determine intervals of increase and decrease?
4. What are the key characteristics of a cubic function based on its graph?
5. How can you estimate inflection points from a graph?

Tip: To find intervals of increasing and decreasing more precisely, you can use the derivative of the function and set it equal to zero to find critical points!