Test function

A test function is a mathematical tool used in analyzing or verifying the properties of other functions or systems. It acts like a probe or a lens, allowing us to examine how a system responds to different inputs. By applying a test function, we can determine characteristics like stability, continuity, or other behaviors without directly analyzing the entire system. This approach simplifies complex problems, especially in advanced areas like calculus and functional analysis, making it easier to understand how systems work and ensuring they perform as intended.