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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 $y$-axis.
If a function has even symmetry, the following rule applies: $f(\text{-} x)=f(x).$ The rule comes from the fact that even symmetry is a reflection across the $y$-axis. Therefore, changing the sign of the $x$-value does not affect the function value.