Final Answer:
The interval notation that represents the data graphed below is [7, 13].
Step-by-step explanation:
The interval notation [7, 13] indicates that the values in the interval include both 7 and 13. In mathematical terms, this means that the variable x can take any value greater than or equal to 7 and less than or equal to 13. The square brackets [ ] denote that the endpoints 7 and 13 are included in the interval. The absence of parentheses implies inclusivity. Therefore, any real number between and including 7 and 13 is part of the solution set.
In contrast, if the interval notation were (7, 13), with parentheses, it would exclude the endpoints 7 and 13. The notation (7, 13] would exclude 7 but include 13, while [7, 13) would include 7 but exclude 13. The choice of interval notation depends on whether the endpoints are considered part of the solution set. In this case, since the graphed data includes both 7 and 13, the correct interval notation is [7, 13].
Interval notation expresses a range of values. In the options you provided:
1. (7, 13]
- This represents an open interval from 7 to 13, including 13.
2. [7, 13]
- This represents a closed interval from 7 to 13, including both 7 and 13.
3. [7, 13)
- This represents a closed interval from 7 to 13, including 7 but not 13.
4. (7, 13)
- This represents an open interval from 7 to 13, excluding both 7 and 13.
In summary, understanding interval notation is crucial for precisely expressing the range of values a variable can take. The brackets and parentheses convey whether the endpoints are included or excluded, providing a concise and standardized way to represent mathematical intervals.