The option with the role of the plants in the carbon-oxygen cycle is the one that says: they release oxygen into the air as a waste product of photosynthesis.
The question can be answered by looking at the photosynthesis equation:
photosynthesis equation
6CO2 + 12 H2O + Light ------> C6H12O6 + 6O2 + 6H2O
The Plants are related to the carbon-oxygen cycle by the process of photosynthesis that is the form that these organisms get energy to survive and make food since they are autotrophs. The plant take CO2 from the atmosphere, with light and water to convert these molecules into glucose (energy/food), water, and oxygen. The oxygen from photosynthesis is released into the atmosphere and into the oxygen cycle, while de carbon dioxide that is take in the begining is part of the natural carbon cycle.