Question

if an organism reproduces asexually, its offspring will most likely be...
genetically identical to the parent
a mutant
produced from specialized cells known as gametes
genetically different from each other

Explanation:

Asexual reproduction involves only one parent. There is no fusion of gametes (unlike sexual reproduction). The offspring are produced by mitotic division (in many cases). Mitosis results in daughter cells (and thus offspring in asexual reproduction) that have the same genetic material as the parent cell (parent organism). Mutants would require some genetic change (like mutation during DNA replication which is rare and not a characteristic outcome). Gametes are involved in sexual reproduction. And since there's no genetic recombination (as in sexual reproduction with two parents), offspring are not genetically different from each other.

Answer:

genetically identical to the parent