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.
Y-Axis – acts like a mirror
Origin – If you spin the picture upside down
about the Origin, the graph looks the same!
Origin
Even Function!
Odd Function!
Neither!
Even and Odd Functions - Practice Problems
A. Graphically determine whether the following functions are Even, Odd, or Neither
1. 2. 3.
B. Algebraically determine whether the following functions are Even, Odd, or Neither
1.
2.
3.
4.
5.
6.
7.
+ 4
8.
9.
10.
Answers:
Section A (Graphs) Section B (Algebra)
1. Odd 1. Neither
2. Neither 2. Even
3. Even 3. Odd
4. Neither
5. Even
6. Neither
7. Even
8. Even
9. Odd
10. Odd
