Functions

Bijective

A function that is both surjective and injective.

Codomain

Concave

A function is concave if:

f(\alpha x + (1 - \alpha) y) \geq \alpha f(x) + (1 - \alpha) f(y)

See also: convex

Continuous

Convex

A function is convex if:

f(\alpha x + (1 - \alpha) y) \leq \alpha f(x) + (1 - \alpha) f(y)

x^2 is an example of a convex function.

See also: concave

Domain

The set of points the function is defined for.

Image

Injective

A function is injective if it never maps two different inputs to the same output.

See also: surjective, bijective

Monotonic

A function is monotonic if it is non-decreasing or non-increasing.

Surjective

A function is surjective if, for every possible output, there is one input that produces that output.

See also: injective, bijective