The graph in the image shows a piecewise function, and the task is to determine its domain and range. Let's go step by step:

1. Domain:

The domain represents all the possible x-values for which the function is defined.

• The graph starts at $x = -5$ and ends at $x = 4$, with a closed dot at $x = -5$ and an open dot at $x = 4$.
• This means the function is defined from $x = -5$ to $x = 4$, but it does not include $x = 4$ due to the open dot.

So, in interval notation, the domain is: $\boxed{[-5, 4)}$

2. Range:

The range represents all the possible y-values of the function.

• The function's minimum y-value is $y = -2$ (with a closed dot at this point), and the maximum y-value is $y = 3$ (with an arrow going upwards, indicating the function extends beyond this point).
• Therefore, the function covers all y-values from $-2$ to infinity.

So, in interval notation, the range is: $\boxed{[-2, \infty)}$

Would you like more details or have any questions about this solution?

Related Questions:

1. How do you find the range of a function when the graph goes to infinity?
2. How do you interpret open and closed dots on a graph in terms of domain?
3. How does the behavior of the function at the ends affect the range?
4. What is the difference between the domain and range of a function?
5. How would the domain change if the graph had a break or gap in the middle?

Tip:

To determine the domain, always look for the smallest and largest x-values on the graph, and whether the endpoints are included (closed) or not (open).