Even and Odd Functions
A Function can be classified as Even, Odd or Neither. This classification can be
determined graphically or algebraically.
Graphical Interpretation -
Even Functions: Odd Functions:
Have a graph that is Have a graph that is
symmetric with respect symmetric with respect
to the Y-Axis. to the Origin.
Algebraic Test – Substitute
in for everywhere in the function and analyze the
results of
by comparing it to the original function
Even Function:
is Even when, for each in the domain of
,
Odd Function:
is Odd when, for each in the domain of
,
Examples:
a.
b.
c.
Origin – If you spin the picture upside down
about the Origin, the graph looks the same!