In the 1930s and 1940s, engineers like Harry Nyquist and Ralph Hartley developed the use of rational functions as transfer functions to model and analyze electrical circuits and feedback control systems. By expressing system behavior as ratios of polynomials in the complex frequency variable S, they could predict stability and design circuits that respond precisely. Learning rational functions opens the door to understanding control systems, where transfer functions describe how inputs are transformed into outputs, crucial for designing everything from industrial automation to self-driving cars.