Final answer:
The characteristic shared by both prokaryotic and eukaryotic organisms is the need for a source of energy. This is essential for all life forms to carry out their biological functions. Option C is correct.
Step-by-step explanation:
The characteristic shared by all prokaryotic and eukaryotic organisms is C. The need for a source of energy. Both types of cells, irrespective of their complexity, must obtain energy to survive, grow, and reproduce. This energy can come from various sources, such as sunlight (for photosynthetic organisms) or chemicals (in the case of chemotrophs).
Even though prokaryotic cells like E. coli are more simplistic and lack membrane-bound organelles, they still require energy just like the more complex eukaryotic cells found in protozoans, algae, fungi, plants, and animals.
It is essential to note that while both cell types require energy, the ways they attain and utilize this energy can differ. For instance, not all prokaryotic or eukaryotic cells can make their own food (option A), and not all reproduce asexually (option B), nor do all have complex organ systems (option D). However, the necessity for energy is a universal trait across all forms of life.