Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![## Understanding Interval Notations
In mathematics, interval notation is a commonly used notation for expressing subsets of the real numbers, and particularly for expressing the solutions sets of inequalities. Here, we are given a set of options and asked to determine which interval notation correctly represents the inequality \(-3 ≤ x ≤ 3\).
### Given Question and Options:
**Which interval notation represents \(-3 ≤ x ≤ 3\)?**
1) \([-3, 3]\)
2) \((-3, 3]\)
3) \([-3, 3)\)
4) \((-3, 3)\)
### Multiple Choice Answers:
- **a. 1**
- **b. 2**
- **c. 3**
- **d. 4**
### Explanation:
- **Closed Interval Notation \([-3, 3]\):** This notation includes both endpoints \(-3\) and \(3\). It means \(-3 ≤ x ≤ 3\).
- **Half-Closed Interval Notations \((-3, 3]\) and \([-3, 3)\):** These notations include only one endpoint. \((-3, 3]\) includes \(3\) but not \(-3\), and \([-3, 3)\) includes \(-3\) but not \(3\).
- **Open Interval Notation \((-3, 3)\):** This notation does not include either endpoint. It means \(-3 < x < 3\).
The given inequality \(-3 ≤ x ≤ 3\) corresponds to the closed interval \([-3, 3]\).
### Correct Answer:
**a. 1**
### Summary:
To correctly represent the inequality \(-3 ≤ x ≤ 3\), you should use the closed interval notation \([-3, 3]\). This interval includes both the endpoints, aligning with the given inequality.](https://content.bartleby.com/qna-images/question/4ed0702b-be25-4e8d-bf00-15df157283ad/16ef740c-cee3-4686-a486-fdf8c0516baa/1nswwyg_processed.jpeg)
Transcribed Image Text:## Understanding Interval Notations
In mathematics, interval notation is a commonly used notation for expressing subsets of the real numbers, and particularly for expressing the solutions sets of inequalities. Here, we are given a set of options and asked to determine which interval notation correctly represents the inequality \(-3 ≤ x ≤ 3\).
### Given Question and Options:
**Which interval notation represents \(-3 ≤ x ≤ 3\)?**
1) \([-3, 3]\)
2) \((-3, 3]\)
3) \([-3, 3)\)
4) \((-3, 3)\)
### Multiple Choice Answers:
- **a. 1**
- **b. 2**
- **c. 3**
- **d. 4**
### Explanation:
- **Closed Interval Notation \([-3, 3]\):** This notation includes both endpoints \(-3\) and \(3\). It means \(-3 ≤ x ≤ 3\).
- **Half-Closed Interval Notations \((-3, 3]\) and \([-3, 3)\):** These notations include only one endpoint. \((-3, 3]\) includes \(3\) but not \(-3\), and \([-3, 3)\) includes \(-3\) but not \(3\).
- **Open Interval Notation \((-3, 3)\):** This notation does not include either endpoint. It means \(-3 < x < 3\).
The given inequality \(-3 ≤ x ≤ 3\) corresponds to the closed interval \([-3, 3]\).
### Correct Answer:
**a. 1**
### Summary:
To correctly represent the inequality \(-3 ≤ x ≤ 3\), you should use the closed interval notation \([-3, 3]\). This interval includes both the endpoints, aligning with the given inequality.
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