The graph in the image appears to show a function with critical points where it changes its behavior from increasing to decreasing or vice versa. To determine where the function is increasing or decreasing, let's analyze the slope of the curve.

1. Increasing: A function is increasing when the slope of the curve is positive, meaning the function moves upwards as we go from left to right.

2. Decreasing: A function is decreasing when the slope is negative, meaning the function moves downwards as we go from left to right.

From the graph:

• The function starts at the far left of the graph (negative x-values), increasing until it reaches its first peak (local maximum) around $x = -2$.
• After this point, the function decreases between $x = -2$ and $x = 1$ (local minimum).
• Then the function increases again between $x = 1$ and $x = 2$ (local maximum).
• Finally, it decreases after $x = 2$.

Conclusion:

• The function is increasing on the intervals: $(-\infty, -2) \cup (1, 2)$.
• The function is decreasing on the intervals: $(-2, 1) \cup (2, \infty)$.

Would you like more details on the analysis of increasing and decreasing intervals?

Here are 5 related questions to deepen your understanding:

1. What is the formal definition of increasing and decreasing functions?
2. How do you find the critical points of a function analytically?
3. How can you determine the concavity of a function from its graph?
4. How are local maxima and minima related to increasing and decreasing behavior?
5. What is the relationship between the first derivative and increasing/decreasing intervals?

Tip: The first derivative of a function tells you whether a function is increasing or decreasing—positive values indicate increasing, while negative values indicate decreasing.