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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Question
![**Instructions:**
Use the guidelines of this section to sketch the curve.
**Equation:**
\[ y = \frac{x^2 - 25}{x^2 - 5x} \]
**Graphs and Descriptions:**
1. **Top Left Graph:**
- The graph features a curve with a vertical asymptote and a hyperbolic shape. The curve approaches the y-axis asymptotically from both the top and bottom.
- It starts close to -10 on the y-axis, dips down, and approaches the x-axis asymptotically as x increases.
- There is an open circle around \( x = 5 \) indicating a removable discontinuity.
2. **Top Right Graph:**
- This graph shows a straight diagonal line with a positive slope.
- The line extends from the bottom left to the top right.
- A small open circle is present around \( x = 5 \) indicating a discontinuity at this point.
3. **Bottom Left Graph:**
- The graph displays a curve with a vertical asymptote similar to the top left but mirrored horizontally.
- The curve starts near -10 on the x-axis, dips up, and approaches the y-axis asymptotically from both sides.
- There is an open circle around \( x = 5 \).
4. **Bottom Right Graph:**
- Similar to the top right, this graph also shows a straight diagonal line with a positive slope.
- The line extends from the bottom left to the top right without an indicated discontinuity.
**Submit Answer Button:**
A button labeled "Submit Answer" is present below the graphs for user interaction.
**Note:**
Evaluate each graph for accuracy when sketching the behavior of the function provided. Consider vertical and horizontal asymptotes, intercepts, and points of discontinuity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a99fabf-a31f-4250-98b6-bdb0c3640967%2F0600a1c1-83d9-461b-8aea-16baa2d2413e%2Fcemblpn_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Use the guidelines of this section to sketch the curve.
**Equation:**
\[ y = \frac{x^2 - 25}{x^2 - 5x} \]
**Graphs and Descriptions:**
1. **Top Left Graph:**
- The graph features a curve with a vertical asymptote and a hyperbolic shape. The curve approaches the y-axis asymptotically from both the top and bottom.
- It starts close to -10 on the y-axis, dips down, and approaches the x-axis asymptotically as x increases.
- There is an open circle around \( x = 5 \) indicating a removable discontinuity.
2. **Top Right Graph:**
- This graph shows a straight diagonal line with a positive slope.
- The line extends from the bottom left to the top right.
- A small open circle is present around \( x = 5 \) indicating a discontinuity at this point.
3. **Bottom Left Graph:**
- The graph displays a curve with a vertical asymptote similar to the top left but mirrored horizontally.
- The curve starts near -10 on the x-axis, dips up, and approaches the y-axis asymptotically from both sides.
- There is an open circle around \( x = 5 \).
4. **Bottom Right Graph:**
- Similar to the top right, this graph also shows a straight diagonal line with a positive slope.
- The line extends from the bottom left to the top right without an indicated discontinuity.
**Submit Answer Button:**
A button labeled "Submit Answer" is present below the graphs for user interaction.
**Note:**
Evaluate each graph for accuracy when sketching the behavior of the function provided. Consider vertical and horizontal asymptotes, intercepts, and points of discontinuity.
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