https://file.aiquickdraw.com/mathbot/file/1729877561610uggen78a.jpg

The graph displayed in the image shows an interval marked between 1 (an open circle) and 5 (a closed circle) on the number line. 

- The open circle at 1 indicates that the interval does not include 1.
- The closed circle at 5 means that the interval includes 5.

Therefore, the correct notation for this interval is \( (1, 5] \). This is called a "half-open" or "half-closed" interval.

Would you like further details on this concept or have any questions? 

Here are 5 related questions to further explore:

1. What is the difference between open, closed, and half-open intervals?
2. How do you represent intervals on a number line?
3. Can you explain interval notation and its applications in inequalities?
4. What happens when both ends of an interval are open or closed?
5. How are intervals used in functions and calculus?

**Tip:** Always pay attention to whether circles on a graph are open or closed, as they define whether endpoints are included in an interval.

Explore how to interpret the interval (1, 5] on a number line, with open and closed circles indicating whether endpoints are included. Learn about half-open intervals and their significance in mathematics. This guide is perfect for students in Grades 6-8.

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