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Concept

Even Symmetry

If a function has a symmetry, it is either even or odd. The symmetry is even when the graph is symmetric with respect to the -axis.
If a function has even symmetry, the following rule applies:
The rule comes from the fact that even symmetry is a reflection across the -axis. Therefore, changing the sign of the -value does not affect the function value.

The concept applies both ways. Hence, if the rule is true for the entire domain, the function has even symmetry.

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