Monotonic function

Monotonic function is like a very simple game where you can only go up or down, and never come back to where you were before. Imagine you have a bunch of numbers on a line, and you are playing a game where you start at one number and can only move to a higher number or a lower number but not the same number. A monotonic function is the same: it is a math rule that says if you give it a number to start with, it will only give you a number that is higher or lower, but never the same number it started with. It's like going up a hill - you can only go up or down, but you can't stay in the same place. Monotonic function is useful in math because it helps us understand how numbers change over time, and we can use it to make predictions about what will happen next.