Final answer:
The best technique for mapping specific brain functions is the functional magnetic resonance imaging (fMRI), which allows for high-resolution mapping of active brain areas during tasks without exposing the brain to radiation.
Step-by-step explanation:
The technique surgeons use in mapping brain areas responsible for specific activities, such as movement or speech, is functional magnetic resonance imaging (fMRI). This variant of the standard MRI measures changes in brain tissue over time, associated with different activities, making it ideal for creating a detailed map of the brain's functional areas. Unlike standard MRI, fMRI measures changes in the tissue in time with an experimental condition or event, generating a map of the most active areas in the brain.
While other techniques like positron emission tomography (PET) and electroencephalogram (EEG) also monitor brain activity, fMRI is superior due to its ability to create a three-dimensional map of blood flow changes in the brain, which correlates with neuronal activity. This allows for a high-resolution, precise localization of functions such as speech and movement within the brain. fMRI's non-invasive nature, absence of radiation exposure, and temporal resolution make it a preferred method for brain mapping in live patients.