Can you explain why the presence of three types of pigments (chlorophyll a, chlorophyll b, and carotenoids) increase the functioning of photoautotrophs?

Photoautotrophs are organisms, typically a plant, that obtains energy from the sun to be able to convert inorganic materials to organic materials for cellular functions to take place such as biosynthesis and respiration. Its function is increased by the presence of the three types of pigments namely chlorophyll A and B and carotenoids because these are "enablers" of photosynthesis.

The chlorophyll serves as the stepping stone for the sunlight "energy-capture" . This pigment contains porphyrin ring through which electrons can freely to move. Since they move freely, the ring has the ability to gain or lose electrons easily thus they also have the ability to provide energized electrons to other molecules.

However, the carotenoids are accessory pigments only because they cannot directly transfer the energy from the sun to the photosynthetic pathway which means that the absorbed energy must be passed on to chlorophyll first.

Yes they are correct good day