Piecewise Continuous Functions

A piecewise continuous function is a function made up of different parts, or segments, each of which is continuous within its interval—meaning no sudden jumps or gaps. Imagine a graph that looks smooth in sections but might have a break or jump at certain points when moving from one segment to another. These functions are common in real-world situations where changes happen suddenly but smoothly within specific ranges, like tax brackets or temperature thresholds. Overall, piecewise continuous functions are useful for modeling situations with different behaviors across different conditions or intervals.