What is the function of the rough endoplasmic reticulum?

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This may seem like a biology question, but the anatomy & physiology section of the HESI A2 will include a question or two about cell organelles, since the cell is the basic unit of life and the building block of tissues and organs. With that in mind, here is a brief overview of the major cell organelles and their functions:
Cell membrane: Protects the cell, aids in communication with other cells, and regulates the passage of substances into and out of the cell. It is also sometimes called the plasma membrane.
Mitochondria: The "powerhouse" of the cell; the site of cellular respiration and energy production.
Nucleus: Contains the hereditary material (DNA) of the cell in organized masses called chromosomes. The nucleus is the brain of the cell.
Ribosomes: Synthesize (make) proteins. They are found in the cytoplasm and on the rough endoplasmic reticulum.
Rough Endoplasmic Reticulum: Covered in ribosomes and assists in protein synthesis and membrane production.
Smooth Endopasmic Reticulum: The part of the ER not covered in ribosomes, it functions in the detoxification and metabolism of molecules in the cell.
Golgi Apparatus: Packages and transports proteins and lipids throughout the cell. This is the cell's post office.
Lysosomes: Lysosomes are full of hydrolytic enzymes that digest and break down cell waste.
Vacuoles: membrane-enclosed structures that take in food (through a process called phagocytosis) and store it in the cell.
Below is a diagram of a eukaryotic cell with its organelles labeled. 
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What Is the Function of the Rough Endoplasmic Reticulum