https://file.aiquickdraw.com/mathbot/file/1729207034759ix27a2os.jpg

The graph in the image shows a function with a curve that has both a minimum and a maximum, and it appears to be restricted by certain endpoints.

### To determine the **range** of the function:

1. **Lowest point** (minimum):
   - The graph reaches its lowest value at approximately \( y = -9 \).

2. **Highest point** (maximum):
   - The highest point on the graph is around \( y = 7 \), as indicated by the peak of the curve.

3. **End behavior**:
   - There is an endpoint on the right side at \( x \approx 3.5 \), with the corresponding \( y \approx 5 \).

Thus, the **range** of the graph is the set of all \( y \)-values the function takes. Based on the visual inspection, the range is:
\[
y \in [-9, 7]
\]
This means the function's output values range from -9 (inclusive) to 7 (inclusive).

Would you like any further details or explanations? Here are some follow-up questions to consider:

1. How is the range of a function different from the domain?
2. Can a function have an infinite range?
3. How would the range change if the graph continued beyond its current endpoints?
4. What is the relationship between the graph's local minima/maxima and its range?
5. How do horizontal asymptotes affect the range of a function?

**Tip**: The range of a function depends on the lowest and highest points the graph reaches on the vertical axis.

Determine the range of the following graph:

Learn how to determine the range of a function by interpreting a graph. The graph shows a function with a minimum at y = -9 and a maximum at y = 7. Explore key concepts in functions and graph interpretation. Suitable for students in Grades 9-12.

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