Definition:
We say that a function  $f$  has even  symmetry with respect to $x=h$ ("axis reflective symmetry") for a set  D, if whenever $x_a=h+a \in D$ , $x_{-a}=h-a \in D$ and  $f(h-a) = f(h+a)$.
We say that a function  $f$  has odd  symmetry with respect to the point $(h,k)$ for a set  D, if whenever $x_a=h+a \in D$ , $x_{-a}=h-a \in D$ and  $f(h-a) - k = k - f(h+a)$.
 Graph Mapping Diagram $f$  has even  symmetry with respect to $x=h$: $f(h-a) = f(h+a)$ $f$  has odd  symmetry with respect to the point $(h,k)$: $f(h-a) - k = k-f(h+a)$.