Properties of Functions

Functions can either be constant, increasing as $x$ increases, or decreasing as $x $ increases.

Relative minima and maxima are points of the smallest and greatest values in their neighborhoods respectively.

A piecewise function is defined by multiple subfunctions that are each applied to separate intervals of the input

A one-to-one function, also called an injective function, never maps distinct elements of its domain to the same element of its codomain.

Two objects have symmetry if one object can be obtained from the other by a transformation.

Functions that have an additive inverse can be classified as odd or even depending on their symmetry properties.