To determine the domain and range of the function based on the graph provided:

1. Domain: The domain refers to the set of all possible $x$-values for which the function is defined.

   • From the graph, the function appears to start at $x = -4$ and ends at $x = 2$. There is an open circle at $x = 2$, indicating that the function is not defined at this point.

   Domain in interval notation: $[-4, 2)$

2. Range: The range refers to the set of all possible $y$-values that the function can take.

   • The highest point on the graph (the maximum $y$-value) is at $y = 3$, and the lowest point seems to go down indefinitely (negative infinity) as $x$ approaches 2 from the left.

   Range in interval notation: $(-\infty, 3]$

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. How do you determine if a function is continuous based on its graph?
2. What are the differences between open and closed intervals in domain and range?
3. How does the presence of a maximum or minimum point affect the range of a function?
4. How would you describe the behavior of the function as $x$ approaches -4 or 2?
5. What happens to the range if the graph includes a horizontal asymptote?

Tip: Always pay attention to open and closed circles on the graph; they indicate whether a value is included in the domain or range.