Monotonic function
![Figure 1. A monotonically increasing function. It is strictly increasing on the left and right while just non-decreasing in the middle.](/Images/godic/202502/13/Monotonicity_example15434.png")
![Figure 2. A monotonically decreasing function](/Images/godic/202502/13/Monotonicity_example25434.png")
![Figure 3. A function that is not monotonic](/Images/godic/202502/13/Monotonicity_example35434.png")
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.