Determine whether the graph is symmetric with respect to the -axis, -axis, and the origin.

Select all that apply.
A. origin
B. -axis
C. -axis

Ask by Turner Mccarthy. in the United States

Jan 25,2025

Question

Determine whether the graph is symmetric with respect to the -axis, -axis, and the origin.

Select all that apply.
A. origin
B. -axis
C. -axis

Ask by Turner Mccarthy. in the United States

Jan 25,2025

UpStudy AI · Accepted Answer

To determine the symmetries of the graph given by the equation $$ 6x^{2} - 9y^{2} = 7 $$, we'll analyze each type of symmetry individually.

### 1. **Symmetry with Respect to the $$ y $$-axis:**
To test for $$ y $$-axis symmetry, replace $$ x $$ with $$ -x $$ in the equation:
$$
6(-x)^{2} - 9y^{2} = 6x^{2} - 9y^{2} = 7
$$
The equation remains unchanged, indicating that the graph is symmetric with respect to the $$ y $$-axis.

### 2. **Symmetry with Respect to the $$ x $$-axis:**
To test for $$ x $$-axis symmetry, replace $$ y $$ with $$ -y $$ in the equation:
$$
6x^{2} - 9(-y)^{2} = 6x^{2} - 9y^{2} = 7
$$
Again, the equation remains unchanged, indicating symmetry with respect to the $$ x $$-axis.

### 3. **Symmetry with Respect to the Origin:**
To test for origin symmetry, replace both $$ x $$ with $$ -x $$ and $$ y $$ with $$ -y $$:
$$
6(-x)^{2} - 9(-y)^{2} = 6x^{2} - 9y^{2} = 7
$$
The equation remains the same, confirming origin symmetry.

### **Conclusion:**
All three symmetries apply to the graph of the equation $$ 6x^{2} - 9y^{2} = 7 $$.

**Answer:**  
All of the above symmetries apply.

- [x] A. origin
- [x] B. $$ y $$-axis
- [x] C. $$ x $$-axis
The graph is symmetric with respect to the $$ y $$-axis, $$ x $$-axis, and the origin. **Answer:** A. origin B. $$ y $$-axis C. $$ x $$-axis

Determine whether the graph is symmetric with respect to the -axis, -axis, and the origin.

Select all that apply.
A. origin
B. -axis
C. -axis

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Determine whether the graph is symmetric with respect to the -axis, -axis, and the origin. Select all that apply. A. origin B. -axis C. -axis

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Determine whether the graph is symmetric with respect to the -axis, -axis, and the origin.

Select all that apply.
A. origin
B. -axis
C. -axis