Definition: We say that a function  $f$  has even  symmetry ("Y-axis reflective symmetry") for a set  D, if whenever $a \in D$ , $-a \in D$ and $f(-a) = f(a)$.
We say that a function  $f$  has odd  symmetry ("origin symmetry") for a set  D, if whenever $a \in D$ , $-a \in D$ and  $f(-a) = -f(a)$.

	Graph	Mapping Diagram
$f$  has even  symmetry: $f(-a) = f(a)$
$f$  has odd  symmetry: $f(-a) = -f(a)$.

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  $f(h-a) - k  = -(f(h+a) - k)$.