Question

Any curve in 2D that is symmetric about the origin is also symmetric with respect to both the axes
Is the statement true? Give reason for your answers either with a
short proof or a counterexample.

Answer 1

Answer on Question #78760 – Math – Analytic Geometry

Question

Any curve in 2D that is symmetric about the origin is also symmetric with respect to both the axes. Is the statement true? Give reason for your answers either with a short proof or a counterexample.

Solution

The statement is false.

Counterexample: $f(x) = x^3$.

The graph is symmetric about the origin, but it is not symmetric about any of the axes.

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