https://file.aiquickdraw.com/mathbot/file/1729102071542tmco8ng2.jpg

Let's analyze each graph and identify the applicable symmetries.

### Graph 1
This graph resembles a sinusoidal (wave) function, which often has symmetry:
- **Y-axis symmetry**: True, as the function appears to mirror across the y-axis.
- **X-axis symmetry**: False, as it does not mirror across the x-axis.
- **Origin symmetry**: False, as it is not symmetric about the origin.
- **Correct Answer**: Only **y-axis** symmetry applies.

### Graph 2
This graph is a straight line passing through the origin with a positive slope, likely representing a linear function like \( y = x \).
- **Y-axis symmetry**: False, as it does not mirror across the y-axis.
- **X-axis symmetry**: False, as it does not mirror across the x-axis.
- **Origin symmetry**: True, as it is symmetric about the origin (rotational symmetry).
- **Correct Answer**: Only **origin** symmetry applies.

### Graph 3
This graph shows a square centered at the origin.
- **Y-axis symmetry**: True, as it mirrors across the y-axis.
- **X-axis symmetry**: True, as it mirrors across the x-axis.
- **Origin symmetry**: True, as it has rotational symmetry about the origin.
- **Correct Answer**: **X-axis, Y-axis, and origin** symmetry all apply.

Let me know if you want more details or have questions!

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Here are some related questions for further exploration:
1. What types of functions typically have origin symmetry?
2. How can you determine x-axis symmetry in a function's graph?
3. What transformations preserve y-axis symmetry?
4. Are there functions with all three symmetries (x-axis, y-axis, and origin)?
5. How does symmetry affect the properties of a function?

**Tip**: Symmetries can often be verified algebraically by testing conditions like \( f(-x) = f(x) \) for y-axis symmetry or \( f(-x) = -f(x) \) for origin symmetry.

For each graph, select all symmetries that apply.

Learn how to identify symmetry in various functions, including sinusoidal, linear, and square graphs. This tutorial covers y-axis, x-axis, and origin symmetry. Suitable for students in Grades 9-12.

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