**The Protein that Functions Outside the Cytosol**

To understand which cellular component is responsible for the production of proteins that function outside the cytosol, we need to examine the different organelles involved in protein synthesis. These organelles include the mitochondria, the rough endoplasmic reticulum (RER), and the nucleus.

**Ribosome in Mitochondria**
The mitochondria are known as the powerhouses of the cell, responsible for generating ATP through cellular respiration. However, they also possess their own ribosomes, known as mitochondrial ribosomes. These ribosomes are responsible for synthesizing proteins required for mitochondrial function. While some of these proteins remain within the mitochondria, others are transported outside to perform various functions. Therefore, the proteins produced by ribosomes in mitochondria may function both within and outside the cytosol.

**Ribosome on Rough Endoplasmic Reticulum (RER)**
The rough endoplasmic reticulum (RER) is studded with ribosomes on its surface. These ribosomes synthesize proteins that are destined for secretion, membrane insertion, or localization to other organelles. The proteins synthesized by ribosomes on the RER are co-translationally translocated across the ER membrane and enter the ER lumen. From there, they are further processed and sorted to their final destinations. These proteins can be secreted outside the cell, incorporated into the plasma membrane, or targeted to other organelles such as the Golgi apparatus. Therefore, the proteins produced by ribosomes on the RER are likely to function outside the cytosol.

**Ribosome in the Nucleus**
The nucleus is responsible for housing the cell's DNA and controlling gene expression. While the nucleus contains ribosomes, they are primarily involved in the synthesis of proteins required for nuclear functions, such as DNA replication and transcription regulation. These proteins generally function within the nucleus itself and are not typically exported outside the cytosol.

Therefore, out of the given options, the proteins that are most likely to function outside the cytosol are made by ribosomes on the rough endoplasmic reticulum (RER). These ribosomes synthesize proteins that are destined for secretion, membrane insertion, or localization to other organelles, allowing them to function in various extracellular or membrane-related processes.

Option C.. its rough endoplasmic reticulum