To determine the domain and range from the graph provided in the image:

1. Domain: The domain is the set of all possible x-values for which the function is defined. In the graph, the function starts at $x = -4$ and ends at $x = 5$. So the domain is the interval from $-4$ to $5$, written in interval notation as: $\text{Domain: } [-4, 5]$

2. Range: The range is the set of all possible y-values that the function attains. From the graph, the y-values range from $-3$ (at the lowest point) to $7$ (at the highest point). So, the range in interval notation is: $\text{Range: } [-3, 7]$

Let me know if you need more details or if you have any questions!

Here are some related questions to further your understanding:

1. How do you find the domain and range of more complex functions?
2. What does it mean when a function is continuous on its domain?
3. Can a function have a domain with gaps (discontinuous)?
4. How would the domain or range change if the graph included an open circle at an endpoint?
5. What are some common types of functions with restricted domains (e.g., square root, rational)?

Tip: Always check both endpoints of the graph carefully, especially if they are open or closed, as this can affect the domain and range.