Determine whether the graph is symmetric with respect to the x-axis, y-axis, and the origin. 3x²-9y² = 2 Select all that apply. A. origin B. x-axis C. y-axis
Determine whether the graph is symmetric with respect to the x-axis, y-axis, and the origin. 3x²-9y² = 2 Select all that apply. A. origin B. x-axis C. y-axis
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 17
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## Determine Graph Symmetry
### Problem Statement
Determine whether the graph is symmetric with respect to the x-axis, y-axis, and the origin.
\[ 3x^2 - 9y^2 = 2 \]
### Question
Select all that apply.
- ☐ A. origin
- ☐ B. x-axis
- ☐ C. y-axis
---
### Explanation
In this problem, we are given a quadratic equation and asked to determine the axes of symmetry and origin symmetry of its graph.
**Steps to Determine Symmetry:**
1. **Symmetry with respect to the y-axis:**
Replace \( x \) with \( -x \) and examine if the equation remains unchanged.
\[ 3(-x)^2 - 9y^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the y-axis.
2. **Symmetry with respect to the x-axis:**
Replace \( y \) with \( -y \) and examine if the equation remains unchanged.
\[ 3x^2 - 9(-y)^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the x-axis.
3. **Symmetry with respect to the origin:**
Replace \( x \) with \( -x \) and \( y \) with \( -y \) and examine if the equation remains unchanged.
\[ 3(-x)^2 - 9(-y)^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the origin.
Therefore, the correct selections are:
- A. origin
- B. x-axis
- C. y-axis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e2935af-1329-4dfa-9560-8781a8a0c5be%2F6b9101fb-cfac-4d70-be5d-3b126439e7fc%2F3slyv2h_processed.png&w=3840&q=75)
Transcribed Image Text:---
## Determine Graph Symmetry
### Problem Statement
Determine whether the graph is symmetric with respect to the x-axis, y-axis, and the origin.
\[ 3x^2 - 9y^2 = 2 \]
### Question
Select all that apply.
- ☐ A. origin
- ☐ B. x-axis
- ☐ C. y-axis
---
### Explanation
In this problem, we are given a quadratic equation and asked to determine the axes of symmetry and origin symmetry of its graph.
**Steps to Determine Symmetry:**
1. **Symmetry with respect to the y-axis:**
Replace \( x \) with \( -x \) and examine if the equation remains unchanged.
\[ 3(-x)^2 - 9y^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the y-axis.
2. **Symmetry with respect to the x-axis:**
Replace \( y \) with \( -y \) and examine if the equation remains unchanged.
\[ 3x^2 - 9(-y)^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the x-axis.
3. **Symmetry with respect to the origin:**
Replace \( x \) with \( -x \) and \( y \) with \( -y \) and examine if the equation remains unchanged.
\[ 3(-x)^2 - 9(-y)^2 = 2 \]
\[ 3x^2 - 9y^2 = 2 \]
The equation remains the same, indicating symmetry with respect to the origin.
Therefore, the correct selections are:
- A. origin
- B. x-axis
- C. y-axis
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