The problem asks us to determine the intervals where the given function is increasing and decreasing, and also the domain of the function. The graph of the function is provided. The x-values on the graph are in steps of 0.5.

1. Problem Description

The problem asks us to determine the intervals where the given function is increasing and decreasing, and also the domain of the function. The graph of the function is provided. The x-values on the graph are in steps of 0.

5.

2. Solution Steps

First, let's identify the intervals where the function is increasing. A function is increasing if its graph goes upwards as we move from left to right. From the graph, the function is increasing from $-\infty$ up to the local maximum at $x = -2.5$ and also from the local minimum at $x = 0.5$ to $\infty$. Therefore, the function is increasing on the intervals $(-\infty, -2.5]$ and $[0.5, \infty)$.

Next, let's identify the intervals where the function is decreasing. A function is decreasing if its graph goes downwards as we move from left to right. From the graph, the function is decreasing from the local maximum at $x = -2.5$ to the local minimum at $x = 0.5$. Therefore, the function is decreasing on the interval $[-2.5, 0.5]$.

Finally, let's determine the domain of the function. The domain is the set of all possible x-values for which the function is defined. From the graph, we can see that the function is defined for all x-values from $-\infty$ to $\infty$. Therefore, the domain of the function is $(-\infty, \infty)$.

3. Final Answer

The function is increasing on the interval(s): $(-\infty, -2.5]$, $[0.5, \infty)$

The function is decreasing on the interval(s): $[-2.5, 0.5]$

The domain of the function is: $(-\infty, \infty)$