Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. x² + y² = 15 Select all that apply.
Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. x² + y² = 15 Select all that apply.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Task: Symmetry in Graphs**
**Instruction:**
Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
\[ x^2 + y^2 = 15 \]
**Options:**
Select all that apply.
- A. x-axis
- B. y-axis
- C. origin
- D. none of these
**Explanation:**
The given equation \( x^2 + y^2 = 15 \) is the equation of a circle centered at the origin with a radius of \(\sqrt{15}\). This type of equation is inherently symmetric with respect to both the x-axis and y-axis, and consequently, also symmetric with respect to the origin.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffafbea1e-da97-44d9-88cf-94bc0d1ddd25%2F436f097e-ce07-416f-a17e-3a3fbfe81697%2Fcs7zqye_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Task: Symmetry in Graphs**
**Instruction:**
Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
\[ x^2 + y^2 = 15 \]
**Options:**
Select all that apply.
- A. x-axis
- B. y-axis
- C. origin
- D. none of these
**Explanation:**
The given equation \( x^2 + y^2 = 15 \) is the equation of a circle centered at the origin with a radius of \(\sqrt{15}\). This type of equation is inherently symmetric with respect to both the x-axis and y-axis, and consequently, also symmetric with respect to the origin.
---
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