The picture above shows that the harmonic functions for chords as:
Tonic: I, III, VI Dominant: V, VII Subdominant: IV, II
Dp these same classification also apply to the natural minor scale?
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Yes. However, chord functions in minor generally assume a raised 7th scale degree (i.e., leading tone). So V in minor is presumed to be a major chord, and VII in minor is presume to be a diminished chord.
When the chords have a lowered seventh (minor V and major VII), although they are generally considered to have the same dominant function, it is a much weaker effect.