Question

Vestigial organs such as the appendix exist because
A. They had an important function during development which is not needed in the adult
B. They have a redundant role to play if an organ with similar function fails
C. Nature cannot get rid of structures that have already formed
D. They were inherited from an evolutionary ancestor in which they were functional

Answer 1

Vestigiality is that the retention during the method of evolution of genetically determined structures or attributes that have lost some or all of the ancestral function in a very given species.

Complete answer:
Human vestigiality involves those traits occurring in humans that have lost all or most of their original function through evolution. Although structures called vestigial often appear functionless, a vestigial structure may retain lesser functions or develop minor new ones.
Vestigiality relies on comparison with homologous features in related species. The emergence of vestigiality occurs by normal evolutionary processes, by loss of function of a feature that's not subject to positive selection pressures. The feature is also selected against more urgently when its function becomes definitively harmful, but if the shortage of the feature provides no advantage, and its presence provides no disadvantage, the feature might not be phased out by natural action and persist across species.
Vestigial structures are often called vestigial organs, although many of them don't seem to be actually organs. Such structures are degenerate, atrophied, or rudimentary, with a tendency to be rather more variable than homologous non-vestigial parts. These organs had played a job in ancestral organisms; however, with evolution such structures retain lesser functions or become adapted to new roles in extant populations.
Appendix
In modern humans, the appendix is a vestige of a redundant organ that in ancestral species had digestive functions, very much like it still does in extant species during which microorganism hydrolyzes cellulose and similar indigestible plant materials.
The human appendix is akin to that of the rabbit's in size, though the caecum is reduced to one bulge where the ileum empties into the colon. Some carnivorous animals may have appendices too, but seldom have quite vestigial caeca.
Intestinal bacterial populations entrenched in the appendix may support quick re-establishment of the flora of the big intestine after an illness, poisoning, or after antibiotic treatment depletes or causes harmful changes to bacterial population in colon.

Therefore, the right option is d, They were inherited from an evolutionary ancestor within which they were functional.

Note: Researchers deduce that the appendix has the power to safeguard good bacteria within the gut. That way, when the gut is stricken by a bout of diarrhea or other illness that cleans out the intestines, the nice bacteria within the appendix can repopulate and keep the person healthy.
Some research in recent times suggests that appendix, which is a vestigial organ guards against the loss of symbiotic bacteria that aid in digestion, though that's unlikely to be a unique function, given the presence of vermiform appendix in many herbivores.