Final answer:
The region of space with the given electric potential V = x^2 + y^2 + 22 is containing charges because a nonzero electric potential suggests the existence of an electric field due to charges.
Step-by-step explanation:
The electric potential in a region of space is given by V = x^2 + y^2 + 22. This potential function suggests that there is a presence of electric charges in the region since an electric potential exists where there are charges. To determine if the space is charge-free or containing charges, one would usually take the gradient of the potential to find the electric field. However, a nonzero electric potential like the one given implies that there must be some electric field, and hence, charges are present. This leads us to conclude that the region is containing charges. This conclusion is supported by the understanding that the electric potential is a result of electric charges, and electric field lines radiate out from positive charges and terminate on negative charges. Based on the given electric potential function, which is not a constant, it changes with position, indicating that it is created by charges within the region.