Let's analyze the graph provided.

1. Increasing Intervals:

The function is increasing where the slope of the curve is positive (the graph moves upwards as we go from left to right).

• The graph increases from $x \approx -4$ to $x = -2$.
• It also increases again from $x = 1$ onwards.

So, the function is increasing on the intervals: $(-4, -2) \cup (1, \infty)$

2. Decreasing Intervals:

The function is decreasing where the slope of the curve is negative (the graph moves downwards as we go from left to right).

• The graph decreases from $x = -2$ to $x = 1$.

So, the function is decreasing on the interval: $(-2, 1)$

3. Domain:

The domain is the set of all possible $x$-values for which the function is defined. Since the graph is continuous from left to right and there are no breaks or gaps, the domain is all real numbers: $(-\infty, \infty)$

Would you like more details or have any further questions?

Here are some related questions to explore:

1. What are the local maxima and minima of the function?
2. How can we find the range of this function from the graph?
3. Can you identify any points of inflection in the graph?
4. What is the behavior of the function as $x \to -\infty$ and $x \to \infty$?
5. How would the graph look if the function was shifted vertically by 2 units?

Tip: When analyzing graphs, always look for points where the slope changes sign to identify increasing or decreasing intervals.