https://file.aiquickdraw.com/mathbot/file/17272334709962teodybc.jpg

Let's examine the symmetries of the graphs:

### Graph 1:
- **Graph type:** A sinusoidal wave, similar to the graph of \( y = \sin(x) \).
- **Symmetry:** 
  - This graph is symmetric about the **origin**, as sine functions are odd functions.
  - It is not symmetric about the **x-axis** or the **y-axis**.

### Graph 2:
- **Graph type:** A circle, centered at the origin.
- **Symmetry:**
  - The circle is symmetric about the **x-axis**, **y-axis**, and the **origin**.

### Graph 3:
- **Graph type:** A parabola, likely representing a sideways parabola (which may be part of the equation \( x = y^2 \)).
- **Symmetry:**
  - This graph is symmetric about the **x-axis**.
  - It is not symmetric about the **y-axis** or the **origin**.

### Summary:
- **Graph 1:** Symmetry at the **origin**.
- **Graph 2:** Symmetry at the **x-axis**, **y-axis**, and **origin**.
- **Graph 3:** Symmetry at the **x-axis**.

Would you like more details or explanations about these symmetries?

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Here are 5 related questions for further learning:
1. What makes a function symmetric about the origin?
2. How can you determine if a graph is symmetric about the x-axis or y-axis algebraically?
3. What are the typical symmetries of trigonometric functions?
4. How can symmetries help simplify graphing and solving equations?
5. What are the characteristics of odd and even functions?

**Tip:** Symmetry about the origin implies that a graph remains unchanged when both the x and y coordinates are negated.

For each graph, select all symmetries that apply.

Explore the symmetry properties of graphs, including sinusoidal waves, circles, and parabolas. Learn to identify symmetries about the x-axis, y-axis, and origin with step-by-step analysis. Suitable for high school students studying advanced algebra and geometry.

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