From the bacterial model:
(a) the tail-like structure is known as the flagellum (plural, flagella)
(b) The primary function of the structure is to aid movement. It is moved in a whip-like version to propel the organism.
(c) Based on the absence of of flagellum in the other two bacteria, it means that they are not motile.
The presence of flagellum in bacteria is an indication that such bacteria are motile. The thread-like structure is whipped randomly in order for the organism to move and the absence of it in an bacterium is an indication that such a bacterium is not motile.
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