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

Solution

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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