Understanding Jump Discontinuity in Functions

Every time you turn your lights on and off, you are essentially using a unit step function. In this article, we will explore this function and other functions with jump discontinuities. For a thorough understanding of continuity, please refer to our article on Continuity. To learn about different types of discontinuities, check out our article on Removable Discontinuity.

An Example of Jump Discontinuity

Let's begin by examining the unit step function, also known as the Heaviside function. This function was initially created by Oliver Heaviside for telegraphy purposes, but it is now commonly used in biology and neuroscience to model cellular switches that respond to chemical signals. The formula for this function is f(x) = 1 for x ≥ 0 and f(x) = 0 for x < 0, and its graph is as follows:

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