To solve the problem, we will analyze the intervals of increase and decrease for the given function $f$, based on the provided graph.

Steps to Determine the Intervals:

1. Identify where the slope is positive (increasing): A function is increasing on an interval if its graph moves upwards as we go from left to right (positive slope).

2. Identify where the slope is negative (decreasing): A function is decreasing on an interval if its graph moves downwards as we go from left to right (negative slope).

3. State the intervals precisely: Use $x$-values to specify the intervals of increase and decrease.

Observing the Graph:

• Decreasing: The function decreases from $x = -10$ to $x = -2$ (segment 1) since the slope is negative.

• Increasing: The function increases from $x = -2$ to $x = 2$ (segment 2) since the slope is positive.

• Decreasing: The function decreases from $x = 2$ to $x = 10$ (segment 3) as the slope is negative again.

Final Answer:

• Increasing Interval: $(-2, 2)$
• Decreasing Intervals: $(-10, -2)$ and $(2, 10)$

Let me know if you'd like further clarification or details! 😊

Additional Questions to Explore:

1. What is the slope of each segment in this graph?
2. How can you determine critical points of the function $f(x)$?
3. What are the consequences of increasing/decreasing behavior for extrema?
4. How can you confirm these intervals using derivatives?
5. What would the graph look like if $f$ were shifted upwards by 3 units?

Tip:

Always examine the graph carefully to check where the slope changes its sign to identify transitions between increasing and decreasing intervals.