Is a function odd, even or neither?
Compare
- Even:
, giving symmetry in the -axis. - Odd:
, giving symmetry about the origin. - If neither identity holds, the function is neither. The domain must also be symmetric about zero.
Example 1
Even powers
Determine whether the function is odd, even or neither.
Example 2
An odd power with a constant
Classify the function as odd, even or neither, showing your reasoning.
Remember
Odd/even function symmetry is different from whether the polynomial’s degree is odd or even. The zero function is both odd and even.
Your turn
Classify the function as odd, even or neither.
Check answer
Classify the function as odd, even or neither.
Check answer
Classify the function as odd, even or neither.
Check answer
Classify the function as odd, even or neither.
Check answer
Classify the function as odd, even or neither.
Check answer
Classify the function as odd, even or neither.
Classify the function as odd, even or neither.
Classify the function as odd, even or neither.
Classify the function as odd, even or neither.
Classify the function as odd, even or neither.