How do a transistor works as a switch?

Answer:
A transistor operates as a switch by operating it outside of its linear range.

Basically, if you apply less voltage across the base-emitter junction than required to turn in on, then it is off, and if you apply more current through the base-emitter junction than collector-emitter current divided by hFe, then then it is on and saturated, fully outside of its linear range.
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