FIG. 1 is a front perspective view of the multi-function hair comb showing my new design. FIG. 2 is a side view of the multi-function hair comb; FIG. 3 is an opposite side view of the multi-function hair comb; FIG. 4 is a front view of the multi-function hair comb; FIG. 5 is a rear view of the multi-function hair comb; FIG. 6 is a top view of the multi-function hair comb; and, FIG. 7 is a bottom view of the multi-function hair comb.