Derived LF for our full sample of Galactic AGB carbon stars (solid black line, excluding J-type and R-hot stars) compared with the theoretical LFs described in Sect. 3 (red dashed histogram), and with the LF expected for a typical model of an extrinsic C-star (black dotted line; see text). The theoretical LFs are normalised such that the peak of a LF matches the peak of the corresponding observations.