Final answer:
The fader is the component on a mixing console that gives precise control of the volume of each channel. It allows the audio engineer to balance the sound mix by adjusting the loudness of different channels.
Step-by-step explanation:
The component that provides precise control of the volume of each channel on a mixing console is known as the fader. Faders are critical in adjusting the loudness of different sound channels, enabling sound engineers to balance the audio mix effectively. Unlike the function generator mentioned, which controls amplitude and frequency to manipulate sound waves, the fader specifically controls the volume level on a mixing board.
Components like the equalizer would be used to adjust the balance of different frequencies within an audio signal, while a mixer refers to the entire console that might contain faders, equalizers, and other audio processing units. An amplifier, on the other hand, increases the power of an audio signal, making it louder after the signal has been mixed and processed.