Two examples of a formal region might be the US and Canada, while functional regions might be Dubai and Los Angeles, and two examples of a perceptual region might be New York and the US South.
They are fields of study of human geography, being as a definition of a formal region any geographic area that has official and legally recognized limits, defining the place, like every nation in the world.
A functional region can be understood as a territory that is located around a central activity area, for example we have cities, a commercial route or an educational center.
On the other hand, perceptual regions are those that reflect the cultural identity of a population, that is, regions known for behaviors, feelings and characteristics of places or people.
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