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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.

Find the domain and range of the function graphed below in interval notation.

Learn how to find the domain and range of a function based on its graph. This problem demonstrates key concepts in graph analysis, focusing on identifying the correct interval notation for the domain and range. Suitable for students in Grades 8-10.

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