Final answer:
The single-celled organism observed under the microscope is a prokaryote, which lacks a nucleus and has a cell wall, indicating that it belongs to either domain Bacteria or Archaea. The best fit based on provided information is domain Bacteria.
Step-by-step explanation:
When looking at an organism under a microscope that is very small, has a cell wall, and no nucleus, you have identified key characteristics of prokaryotic cells. Since this organism lacks a nucleus it cannot be a member of the domain Eukarya, which includes organisms like plants and animals with membrane-bound nuclei and organelles. Instead, the organism would belong to either domain Bacteria or Archaea, both of which are prokaryotic. Domain Bacteria includes typical prokaryotic cells that we commonly know as bacteria, while domain Archaea comprises prokaryotic cells that often live in extreme environments and have distinct biochemical and genetic properties. Given the options provided, and the description of the organism, the most suitable answer would be domain Bacteria, as these are the common single-celled prokaryotes without a nucleus.