Find the Symmetry x=y^4-y^2

Problem

x=y4−y2

Solution

1. Test for x-axis symmetry by replacing y with −y in the equation.

x=(−y)4−(−y)2

x=y4−y2

Since the equation is unchanged, the graph is symmetric with respect to the xaxis.

2. Test for y-axis symmetry by replacing x with −x in the equation.

−x=y4−y2

x=−y4+y2

Since the equation changed, the graph is not symmetric with respect to the yaxis.

3. Test for origin symmetry by replacing x with −x and y with −y in the equation.

−x=(−y)4−(−y)2

−x=y4−y2

x=−y4+y2

Since the equation changed, the graph is not symmetric with respect to the origin.

Final Answer

Symmetry: *x*-axis

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