Relative To An Operator (c.q. A Group or Other Structure)
These properties concern how the function is affected by arithmetic operations on its operand.
The following are special examples of a homomorphism on a binary operation:
- Additive function: preserves the addition operation: f(x+y) = f(x)+f(y).
- Multiplicative function: preserves the multiplication operation: f(xy) = f(x)f(y).
Relative to negation:
- Even function: is symmetric with respect to the Y-axis. Formally, for each x: f(x) = f(−x).
- Odd function: is symmetric with respect to the origin. Formally, for each x: f(−x) = −f(x).
Relative to a binary operation and an order:
- Subadditive function: for which the value of f(x+y) is less than or equal to f(x)+f(y).
- Superadditive function: for which the value of f(x+y) is greater than or equal to f(x)+f(y).
Read more about this topic: List Of Types Of Functions
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