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The cell membrane primarily controls what goes in and out of the cell, serving as a selective barrier that regulates the movement of substances. This semi-permeable nature allows essential nutrients and molecules to enter the cell while keeping harmful substances out. It also helps maintain the internal environment of the cell by controlling the exchange of ions and water, contributing to homeostasis.
The other options, while related to cell function, do not accurately describe the primary role of the cell membrane. Energy production within the cell occurs in the mitochondria, protein synthesis mainly takes place on ribosomes in the cytoplasm or on the rough endoplasmic reticulum, and the structural integrity of the cell is maintained by the cytoskeleton and the rigidity provided by the cell wall in plants, not the membrane itself.
Thus, the focus of the cell membrane's responsibilities is distinctly related to its role in regulating the passage of materials, making "what goes in and out of the cell" the correct choice.