Questions: Symmetric with respect to the X-axis Symmetric with respect to the Y-axis Symmetric with respect to the origin None of these

Symmetric with respect to the X-axis Symmetric with respect to the Y-axis Symmetric with respect to the origin None of these
Transcript text: Symmetric with respect to the $X$-axis Symmetric with respect to the $Y$-axis Symmetric with respect to the origin None of these
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Solution

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Solution Steps

Step 1: Identify the symmetry of the first graph
  • The first graph is a triangle centered on the Y-axis.
  • Check if the graph is symmetric with respect to the X-axis: No, because the top and bottom parts are not mirror images.
  • Check if the graph is symmetric with respect to the Y-axis: Yes, because the left and right parts are mirror images.
  • Check if the graph is symmetric with respect to the origin: No, because rotating 180 degrees does not produce the same graph.

Final Answer

  • The first graph is symmetric with respect to the Y-axis.
Step 2: Identify the symmetry of the second graph
  • The second graph is a polynomial curve.
  • Check if the graph is symmetric with respect to the X-axis: No, because the top and bottom parts are not mirror images.
  • Check if the graph is symmetric with respect to the Y-axis: No, because the left and right parts are not mirror images.
  • Check if the graph is symmetric with respect to the origin: No, because rotating 180 degrees does not produce the same graph.
Final Answer
  • The second graph has none of the listed symmetries.
Step 3: Identify the symmetry of the third graph
  • The third graph is not provided in the image, so we cannot analyze it.
Final Answer
  • Unable to analyze the third graph due to lack of information.
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