This talk stands on our current work [1], where we establish a determination result for merely bounded from below functions, by adding an assumption controlling the asymptotic behavior. This assumption is trivially fulfilled if f is inf-compact. In addition, the result is not only valid for the (De Giorgi) local slope but also for the main paradigms of average descent operators as well as for the global slope, a case in which the asymptotic assumption becomes superfluous. Therefore, the present work extends simultaneously the metric determination results of [2] and [3]. [1] A. Daniilidis, Tri Minh Le, D. Salas, Metric compatibility and determination in complete metric spaces, https://arxiv.org/abs/2211.11819.  [2] A. Daniilidis, D. Salas, A determination theorem in terms of the metric slope, Proc. Amer. Math. Soc. 150 (2022), 4325–4333.  [3] L. Thibault, D. Zagrodny, Determining functions by slopes, Communications in Contemporary Mathematics 25 (2023), no 7, 2250014.