Step 1: Understand the three domains of life: Bacteria, Archaea, and Eukarya. Each domain represents a major group of organisms distinguished by differences in their cell structure, genetics, and biochemistry.
Step 2: Identify characteristics of organisms in each domain. Bacteria are prokaryotes with peptidoglycan in their cell walls, Archaea are prokaryotes but lack peptidoglycan and often live in extreme environments, and Eukarya are organisms with membrane-bound nuclei and organelles.
Step 3: Match each example organism to its correct domain by recalling their classification: For example, Escherichia coli is a well-known bacterium (Bacteria), Methanococcus is an archaeon (Archaea), and Saccharomyces cerevisiae is a eukaryotic yeast (Eukarya).
Step 4: Evaluate the given options by checking if the organisms listed under each domain truly belong there based on their taxonomy and characteristics.
Step 5: Confirm that the correct answer lists organisms accurately representing each domain: Bacteria (Escherichia coli), Archaea (Methanococcus), and Eukarya (Saccharomyces cerevisiae).