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 $x$.