https://file.aiquickdraw.com/mathbot/file/1727298757048c02nx8tf.jpg

The graph shown represents a function with its domain and range in need of identification.

### **Domain**:
The domain represents the set of all possible x-values (horizontal axis) that the function can take. From the graph:
- The leftmost point on the curve appears to be at \( x = -6 \), and the rightmost point is at \( x = 5 \).
- The point at \( x = -6 \) is a closed point (filled in), meaning that \( -6 \) is included.
- The point at \( x = 5 \) is an open point (hollow), meaning that \( 5 \) is not included.

Thus, the domain in interval notation is:
\[ [-6, 5) \]

### **Range**:
The range represents the set of all possible y-values (vertical axis) that the function takes. From the graph:
- The lowest point on the curve is at \( y = -6 \), and the highest point is at \( y = 7 \).
- At \( y = -6 \), the point is closed (included), and at \( y = 7 \), the point is open (excluded).

Thus, the range in interval notation is:
\[ [-6, 7) \]

### Final Answer:
- Domain: \([ -6, 5)\)
- Range: \([ -6, 7)\)

Do you want more details or have any questions?

Here are 5 related questions you might want to explore:
1. How do you determine if a point is open or closed on a graph?
2. What is the significance of interval notation in calculus?
3. How would the domain and range change if the graph extended further?
4. Can a function have an infinite range or domain? What would that look like?
5. How does continuity of the function affect its domain and range?

**Tip**: Closed intervals like \([a, b]\) include the endpoints, while open intervals \((a, b)\) exclude them.

Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Learn how to find the domain and range of a function using its graph. This problem covers key concepts such as graphing functions, interpreting domain and range, and using interval notation. Suitable for students in Grades 9-12.

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