https://file.aiquickdraw.com/mathbot/file/1725810341006pzk6vs3f.jpg

The image shows the graph of an equation, which is an ellipse (oval shape), and the question is asking to identify the types of symmetry the graph exhibits.

### Types of symmetry typically considered for graphs:
1. **x-axis symmetry**: The graph is symmetric across the x-axis (if folding the graph along the x-axis results in matching halves).
2. **y-axis symmetry**: The graph is symmetric across the y-axis.
3. **origin symmetry**: The graph is symmetric with respect to the origin (if rotating the graph 180° around the origin results in the same graph).

### Analysis of the graph:
- The graph appears to be an ellipse centered at the origin.
- Ellipses centered at the origin generally have **symmetry about both the x-axis and y-axis**.
- However, ellipses centered at the origin typically do not exhibit **origin symmetry**, as flipping over the origin does not result in an identical graph.

### Conclusion:
For this graph:
- It has **x-axis symmetry** and **y-axis symmetry**.
- It **does not have origin symmetry**.

### Correct answer:
- x-axis
- y-axis

Would you like more details or have any questions on this?

Here are five related questions to further explore the concept:
1. What are the general equations of an ellipse centered at the origin?
2. How can you test for symmetry in different types of functions?
3. What are the types of symmetry that circles exhibit?
4. How does the equation of an ellipse change if it's not centered at the origin?
5. What other conic sections (e.g., parabolas, hyperbolas) exhibit symmetry?

**Tip:** When testing for symmetry, replace variables in the equation (like x with -x or y with -y) to see if the equation remains unchanged!

The graph of an equation is shown. Check ALL the types of symmetry it exhibits.

Explore how to identify symmetry in the graph of an ellipse. Learn about symmetry with respect to the x-axis, y-axis, and the origin, along with the equations of ellipses. Suitable for students in Grades 10-12.

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