4. Sketch the graph of an example function f on domain [0, 10] with jump discontinuities at x = 3 (righ continuous), x = 5 (left continuous), and x = 7 (neither left nor right continuous), where ƒ (3) = 3, ƒ (5) = 5, ƒ (7) = 7.
4. Sketch the graph of an example function f on domain [0, 10] with jump discontinuities at x = 3 (righ continuous), x = 5 (left continuous), and x = 7 (neither left nor right continuous), where ƒ (3) = 3, ƒ (5) = 5, ƒ (7) = 7.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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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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![### Example Function with Jump Discontinuities
**Problem Statement:**
Sketch the graph of an example function \( f \) on the domain \([0, 10]\) with jump discontinuities at:
- \( x = 3 \) (right continuous)
- \( x = 5 \) (left continuous)
- \( x = 7 \) (neither left nor right continuous)
Where:
- \( f(3) = 3 \)
- \( f(5) = 5 \)
- \( f(7) = 7 \)
**Instructions:**
1. **Right Continuous at \( x = 3 \):**
- The function \( f \) approaches the value \( f(3) = 3 \) from the right.
2. **Left Continuous at \( x = 5 \):**
- The function \( f \) approaches the value \( f(5) = 5 \) from the left.
3. **Neither Left nor Right Continuous at \( x = 7 \):**
- The function \( f \) does not approach the value \( f(7) = 7 \) from either direction.
**Graphical Representation:**
- **At \( x = 3 \)**, you would draw the function so that it reaches the value 3 when approached from the right side.
- **At \( x = 5 \)**, you would draw the function so that it reaches the value 5 when approached from the left side.
- **At \( x = 7 \)**, you would draw the function to show a jump discontinuity, indicating that neither side approaches the value 7.
**Visual Explanation:**
Imagine the x-axis ranging from 0 to 10. At points \( x = 3, 5, \) and \( 7 \), there are jumps:
- For \( x = 3 \), the graph would immediately reach 3 when moving from a higher \( x \) value to 3.
- For \( x = 5 \), the graph would immediately reach 5 when moving from a lower \( x \) value to 5.
- For \( x = 7 \), you would see a clear jump that does not align smoothly from either side, reflecting the non-continuity.
By following these instructions and visual guidelines, you will be able to sketch the graph of the described function accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6484a2ba-7b6c-4144-bd9b-1f2d784a131b%2Fbe68af18-b565-4e33-ad15-dafc499424d0%2F54mjwc9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Function with Jump Discontinuities
**Problem Statement:**
Sketch the graph of an example function \( f \) on the domain \([0, 10]\) with jump discontinuities at:
- \( x = 3 \) (right continuous)
- \( x = 5 \) (left continuous)
- \( x = 7 \) (neither left nor right continuous)
Where:
- \( f(3) = 3 \)
- \( f(5) = 5 \)
- \( f(7) = 7 \)
**Instructions:**
1. **Right Continuous at \( x = 3 \):**
- The function \( f \) approaches the value \( f(3) = 3 \) from the right.
2. **Left Continuous at \( x = 5 \):**
- The function \( f \) approaches the value \( f(5) = 5 \) from the left.
3. **Neither Left nor Right Continuous at \( x = 7 \):**
- The function \( f \) does not approach the value \( f(7) = 7 \) from either direction.
**Graphical Representation:**
- **At \( x = 3 \)**, you would draw the function so that it reaches the value 3 when approached from the right side.
- **At \( x = 5 \)**, you would draw the function so that it reaches the value 5 when approached from the left side.
- **At \( x = 7 \)**, you would draw the function to show a jump discontinuity, indicating that neither side approaches the value 7.
**Visual Explanation:**
Imagine the x-axis ranging from 0 to 10. At points \( x = 3, 5, \) and \( 7 \), there are jumps:
- For \( x = 3 \), the graph would immediately reach 3 when moving from a higher \( x \) value to 3.
- For \( x = 5 \), the graph would immediately reach 5 when moving from a lower \( x \) value to 5.
- For \( x = 7 \), you would see a clear jump that does not align smoothly from either side, reflecting the non-continuity.
By following these instructions and visual guidelines, you will be able to sketch the graph of the described function accurately.
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