https://file.aiquickdraw.com/mathbot/file/172953249283918hygcu6.jpg

Let's analyze the symmetry of each graph:

### Graph 1:
- **Description**: This appears to be an ellipse centered at the origin.
- **Symmetries**:
  - **x-axis**: The graph is symmetric about the x-axis.
  - **y-axis**: The graph is symmetric about the y-axis.
  - **Origin**: It is symmetric about the origin as well (since flipping across both axes brings it back to its original shape).

  **Select**: x-axis, y-axis, and origin.

### Graph 2:
- **Description**: This graph seems to represent a rational function with an asymptote.
- **Symmetries**:
  - **x-axis**: Not symmetric about the x-axis.
  - **y-axis**: Not symmetric about the y-axis.
  - **Origin**: It does not seem to have origin symmetry either.
  
  **Select**: None of these.

### Graph 3:
- **Description**: This appears to be a parabola that opens downwards.
- **Symmetries**:
  - **x-axis**: Not symmetric about the x-axis.
  - **y-axis**: The graph is symmetric about the y-axis.
  - **Origin**: Not symmetric about the origin.

  **Select**: y-axis.

### Summary of Answers:
1. **Graph 1**: Select "x-axis," "y-axis," and "origin."
2. **Graph 2**: Select "none of these."
3. **Graph 3**: Select "y-axis."

Would you like further details on why these symmetries apply or have any questions?

### Related Questions:
1. What is the general formula for determining if a function is symmetric with respect to the x-axis?
2. How can you algebraically test for symmetry about the origin?
3. Why do rational functions often have asymptotes that affect their symmetry?
4. What is the relationship between even functions and y-axis symmetry?
5. How does the degree of a polynomial affect its possible symmetries?

### Tip:
For functions symmetric about the origin, if \( f(-x) = -f(x) \), then the function has origin symmetry, often indicating that it’s an odd function.

For each graph, select all symmetries that apply.

Analyze and determine the symmetries of graphs, including ellipses, parabolas, and rational functions. Understand symmetry with respect to the x-axis, y-axis, and origin.

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