Final answer:
Self-feeder protists acquire food primarily through photosynthesis and endocytosis. Photosynthetic protists like euglenas utilize sunlight to make their own food, while protists like amoebas ingest food particles by engulfing them with their cell membrane.
Step-by-step explanation:
The question is asking about the methods by which a self-feeding organism, specifically a self-feeder protist, acquires its food. There are two major ways that self-feeding protists get their food: photosynthesis and endocytosis. In photosynthesis, protists like euglenas and algae use sunlight to create their own food. They are called photoautotrophs and include plant-like protists that have chloroplasts for capturing light energy.
On the other hand, animal-like protists may use a process called endocytosis, where the cell engulfs food particles forming a food vacuole. This method is used by protists such as amoeba, which extend their cell membrane around their prey to ingest it.