In general what are dry chemical fire extinguishers designated to do?

Fire needs three things to burn: fuel, oxygen, and heat. Take away one or more of those three things in sufficient quantities, and the fire can no longer burn.

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A dry chemical fire extinguisher sprays a noncombustible, air resistant layer of foam designed to cover the fire's fuel source. When the fuel source (wood, oil, cloth, etc.) is completely and properly smothered, the expelled dry chemical foam isolates the fuel from the surrounding air, and thereby starves the fire of the oxygen it needs to burn.