Monotonic function

In algebra, a montonic function is any function whose gradient never changes sign. In simple words, it is a function which is either always increasing or decreasing. For example, sin x=f(x) isn't a monotonous function or simply, non monotonous function. That is to say there are no turning points but there may be stationary points where the gradient is momentarily zero. The derivative function of a monotonic function which describes its gradient will never change sign.

Monotonic Function Media

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  Figure 1. A monotonically non-decreasing function.

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  Figure 2. A monotonically non-increasing function

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  Figure 3. A function that is not monotonic

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  Monotonic function with a dense set of jump discontinuities (several sections shown)

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  Plots of 6 monotonic growth functions

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  With the nonmonotonic function "if a then both b and c", false nodes appear above true nodes.

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  Hasse diagram of the monotonic function "at least two of a, b, c hold". Colors indicate function output values.