Jose uses a more serious and professional style of speaking when he is interacting with his professors, but when he is with his friends he uses a much more relaxed style of speaking. what aspect of language is this shifting of speaking styles?

Downward and Upward Style-Shifting

Explanation:

Style-shifting refers to a language style when the speaker change their speech pattern to suit the individual they are speaking to - which can apply to social and cultural dimensions, such as age and the relationship between speakers.

We can clearly see this happening in Jose when he switches his speaking style between his professors (more formal, which is an Upward style-shifting) and between his friends (less formal, which is a Downward style-shifting).