When analyzing functions in a minor key, we must consider the three minor scales: natural, harmonic, and melodic minor. A minor key combines all three of these scales, so any chord that can be constructed with these notes is diatonic. If we were to only use the chords from natural minor, the functions would be: i,iio, III, iv, v, VI, VII. For harmonic minor: i,iio, III+, iv, V, VI, viio. For melodic minor: i, ii, III+, IV, V, vio, viio. (To derive these functions, write out any of the minor scales, and then create triads off every scale degree and remember to use only pitches within the scale as you stack.) When we combine all the available functions from all three minor scales, we have many more diatonic options to work with.
Exercises 1-6 cover the i, iv, v, and V chords. These chords all have a similar function to their major counterparts. The i chord is the tonic, the iv the subdominant, the both the v and V are dominants. The minor v has a much weaker resolution to the tonic than the major V because of the absence of the leading tone in the chord. For example, in C minor, a G major chord resolves strongly to C minor because the leading tone (B) pulls your ear towards the tonic (C). By contrast, the Bb in a G minor chord is a whole-step away from the tonic and does not pull as strongly.
Exercises 7-12 add in the iio and VI chords. The iio still serves as a predominant chord. The VI chord is based off the minor sixth in the scale (in C minor this would be Ab) and can be a temporary resolution just like the vi in major keys. In the context of these exercises, it is the only other major chord besides the V, so it should be easy to identify.
Exercises 13-18 add the III and VII chords. The III represents the tonic in the relative major key, so if it is preceded by a iio or VII, it will sound like you've modulated to the major key. The III can still serve a limited dominant function although it suffers from a weak resolution just as the minor v does (in C minor, the Bb in either chord does not resolve as strongly to C as a leading tone B). The VII is based off the subtonic (minor seventh) scale degree and generally serves as a predominant chord. As you listen to each progression, keep track of the bass movement, the quality of chord (major, minor, etc.), and the function. If you hear a chord and think it is the fourth scale degree, but it is major and also sounds like it has a dominant function, chances are you are really on the fifth scale degree.
