* Archaebacteria: A group of single-celled organisms that were originally classified as bacteria but are now known to be distinct. They are often found in extreme environments.

* Heterotrophic: Organisms that obtain their food from other organisms. They cannot produce their own food through photosynthesis.

* Autotrophic: Organisms that can produce their own food, typically through photosynthesis.

* Saprophytic: Organisms that obtain their food from dead organic matter.

Archaebacteria are not autotrophic. They cannot make their own food through photosynthesis. Instead, they can be either heterotrophic or saprophytic, depending on the specific species:

* Heterotrophic archaebacteria obtain nutrients from other organisms, such as by consuming bacteria or other archaebacteria.

* Saprophytic archaebacteria obtain nutrients from dead organic matter. They play an important role in breaking down organic waste.

Therefore, archaebacteria can be either heterotrophic or saprophytic, but they are not autotrophic.