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.