https://file.aiquickdraw.com/mathbot/file/1726803160650x5qjvyns.jpg

The image contains a mathematical problem asking to determine whether the graph shown is symmetric with respect to the x-axis, the y-axis, and the origin. There are multiple-choice questions for each case.

### Symmetry with respect to the x-axis:
- You selected the answer "No" (A), with the explanation:
  - "No; because when the graph is folded along the x-axis, the parts above and below the x-axis do not coincide."
  - This is **correct**, as the graph is not symmetric about the x-axis. The portions of the graph above and below the x-axis are not mirror images of each other.

### Symmetry with respect to the y-axis:
- There is another question asking about symmetry with respect to the y-axis. Based on the image, you need to identify whether the graph is symmetric when folded along the y-axis.

By observing the shape of the graph, it seems symmetric with respect to the y-axis, meaning if folded along the y-axis, both sides would coincide.

Thus, the correct answer for symmetry with respect to the y-axis is likely **C**: "Yes; because when the graph is folded along the y-axis, the parts to the left and right of the y-axis coincide."

If you'd like a more detailed explanation or have any specific questions, feel free to ask!

### Relative Questions:
1. How do you mathematically check for symmetry with respect to the x-axis in a general function?
2. What are the properties of a function that is symmetric about the y-axis?
3. How can you determine whether a function is symmetric about the origin?
4. What kind of transformations preserve the symmetry of a graph?
5. What types of functions (e.g., even, odd) exhibit symmetry about the y-axis or the origin?

### Tip:
For a function to be symmetric about the y-axis, it must satisfy \( f(x) = f(-x) \) for all \( x \).

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

Learn how to determine if a graph is symmetric with respect to the x-axis, y-axis, and origin. This problem covers key mathematical concepts of graph symmetry and function properties, suitable for Grades 10-12.

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