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

1. Problem Description

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

5.

2. Solution Steps

First, let's determine the intervals where the function is increasing. The function is increasing when its graph rises as we move from left to right along the x-axis. From the graph, we can see that the function is increasing from $x=-5$ to $x=-2.5$ and from $x=0.5$ to $x=3$. Therefore, the intervals where the function is increasing are $[-5, -2.5]$ and $[0.5, 3]$.

Next, let's determine the intervals where the function is decreasing. The function is decreasing when its graph falls as we move from left to right along the x-axis. From the graph, we can see that the function is decreasing from $x=-2.5$ to $x=0.5$. Therefore, the interval where the function is decreasing is $[-2.5, 0.5]$.

Finally, let's find 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 from $x=-5$ to $x=3$. Therefore, the domain of the function is $[-5, 3]$.

3. Final Answer

The function is increasing on the interval(s): [-5, -2.5], [0.5, 3]

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

The domain of the function is: [-5, 3]