This is a special case of the more general notion of a monotonic function.

For monotonic functions in one variable, the range of values is also easy.

It assesses how well the relationship between two variables can be described using a monotonic function.

Also, error variance must be a monotonic function of the specified explanatory variable.

The loss is a monotonic function of the impedance ratio.

The norm may be easily computed from a strictly monotonic moment-generating function.

All other things being equal, an option's theoretical value is a monotonic increasing function of implied volatility.

Obviously the variable can be replaced by any monotonic function, .

The following properties are true for a monotonic function :

An important application of monotonic functions is in probability theory.