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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Do the second one please
 - Appears as a saddle shape extending upwards and downwards.
2.  - Bowl-shaped, opening upwards.
3.  - Sphere centered at the origin.
4.  - Cone extending both upwards and downwards.
5.  - Hyperboloid of one sheet, resembling an hourglass figure.
6.  - Hyperboloid of two sheets, similar to two bowls attached at their bottoms.
---
### Detailed Analysis of the Graphs
- **Graph 1**: This graph shows a saddle-like shape, known as a hyperbolic paraboloid. It typically represents the equation \( z = x^2 - y^2 \).
- **Graph 2**: This graph is a standard paraboloid (bowl shape) opening upwards, which implies the equation \( z = x^2 + y^2 \).
- **Graph 3**: This graph represents a sphere, indicating the equation \( x^2 + y^2 + z^2 = 1 \) or a similar form where all three variables are squared and added up to equal a constant.
- **Graph 4**: This graph shows a double-napped cone, which matches the equation \( z^2 = x^2 + y^2 \).
- **Graph 5**: This graph appears as a hyperboloid of one sheet, an hourglass shape, corresponding to an equation similar to \( x^2 + y^2 - z^2 = 1 \).
- **Graph 6**: This graph is a hyperboloid of two sheets, which denotes an equation similar to \( x^2 + y^2 - z^2 = -1 \).
---
### Matching Equations
1. **Equation 1: \( z = x^2 + y^2 \)**
- **Matching Graph**: Graph 2 (Bowl-shaped paraboloid)
2. **Equation 2: \( 1 = x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ba0aec5-65e2-43b8-bb6a-70de8eae6b73%2F861e051b-28e8-40c8-9761-69e1cbc6b92e%2Fjvu0ub2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matching Equations to Surface Graphs
---
The task is to match the given equations with their corresponding surface graphs.
#### Equations
1. \( z = x^2 + y^2 \)
2. \( 1 = x^2 + y^2 - z^2 \)
#### Surface Graphs
1.  - Appears as a saddle shape extending upwards and downwards.
2.  - Bowl-shaped, opening upwards.
3.  - Sphere centered at the origin.
4.  - Cone extending both upwards and downwards.
5.  - Hyperboloid of one sheet, resembling an hourglass figure.
6.  - Hyperboloid of two sheets, similar to two bowls attached at their bottoms.
---
### Detailed Analysis of the Graphs
- **Graph 1**: This graph shows a saddle-like shape, known as a hyperbolic paraboloid. It typically represents the equation \( z = x^2 - y^2 \).
- **Graph 2**: This graph is a standard paraboloid (bowl shape) opening upwards, which implies the equation \( z = x^2 + y^2 \).
- **Graph 3**: This graph represents a sphere, indicating the equation \( x^2 + y^2 + z^2 = 1 \) or a similar form where all three variables are squared and added up to equal a constant.
- **Graph 4**: This graph shows a double-napped cone, which matches the equation \( z^2 = x^2 + y^2 \).
- **Graph 5**: This graph appears as a hyperboloid of one sheet, an hourglass shape, corresponding to an equation similar to \( x^2 + y^2 - z^2 = 1 \).
- **Graph 6**: This graph is a hyperboloid of two sheets, which denotes an equation similar to \( x^2 + y^2 - z^2 = -1 \).
---
### Matching Equations
1. **Equation 1: \( z = x^2 + y^2 \)**
- **Matching Graph**: Graph 2 (Bowl-shaped paraboloid)
2. **Equation 2: \( 1 = x
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