Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Transcription for Educational Website**
**Task:**
Graph the set \( \{ x \mid -5 < x \leq -3 \} \) on the number line. Then, write the set using interval notation.
**Explanation:**
1. **Number Line Graph:**
- The graph on the number line shows a segment between -5 and -3.
- There is an open circle at -5, indicating that -5 is not included in the set.
- There is a closed circle at -3, indicating that -3 is included in the set.
2. **Interval Notation:**
- The interval is denoted as \((-5, -3]\).
- The parenthesis before -5 indicates that -5 is not included.
- The square bracket after -3 indicates that -3 is included.
3. **Interface Elements:**
- The toolbox includes options to draw open or closed circles and line segments.
- Various notations are presented for creating intervals including open and closed brackets, infinity symbols, and set notation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e73de1c-75a9-4878-87d9-4a2fc0a1762f%2Fb09940a5-1906-407a-aa0c-2b428dab0eb8%2Flb2q3ip_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
**Task:**
Graph the set \( \{ x \mid -5 < x \leq -3 \} \) on the number line. Then, write the set using interval notation.
**Explanation:**
1. **Number Line Graph:**
- The graph on the number line shows a segment between -5 and -3.
- There is an open circle at -5, indicating that -5 is not included in the set.
- There is a closed circle at -3, indicating that -3 is included in the set.
2. **Interval Notation:**
- The interval is denoted as \((-5, -3]\).
- The parenthesis before -5 indicates that -5 is not included.
- The square bracket after -3 indicates that -3 is included.
3. **Interface Elements:**
- The toolbox includes options to draw open or closed circles and line segments.
- Various notations are presented for creating intervals including open and closed brackets, infinity symbols, and set notation.
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