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 $(h,k)$: $f(h-a) - k = k-f(h+a)$.