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Just like bacteria, fungi cannot make their own food. Therefore, fungi are heterotrophs.
Fungi can be parasitic or saprophytic. Parasitic fungi live in or on other living organisms and feed off them. Saprophytic fungi feed on dead and decaying organisms, getting their nutrition from the organisms and breaking them down. For this reason fungi are known as decomposers.
Fungi (just like bacteria) feed by a process called extracellular digestion.
Extracellular means outside the cell and digestion means to break down food into small soluble molecules.
The fungi secrete (produce or discharge) digestive enzymes through their plasma (cell) membrane) onto the food source (e.g. agar on an agar plate or on living things). These digestive enzymes then break down the food into small soluble molecules, such as glucose and amino acids. The small soluble products of digestion are then absorbed across the plasma (cell) membrane back into the hyphae of the fungus where it used in its other life processes, such as respiration.
The diagram below shows the process of extracellular digestion in fungi.