A computer vision system using low-resolution image sensors can provide intelligent services (e.g., activity recognition) but preserve unnecessary visual privacy information from the hardware level. However, preserving visual privacy and enabling accurate machine recognition have adversarial needs on image resolution. Modeling the trade-off of privacy preservation and machine recognition performance can guide future privacy-preserving computer vision systems using low-resolution image sensors. In this paper, using the at-home activity of daily livings (ADLs) as the scenario, we first obtained the most important visual privacy features through a user survey. Then we quantified and analyzed the effects of image resolution on human and machine recognition performance in activity recognition and privacy awareness tasks. We also investigated how modern image super-resolution techniques influence these effects. Based on the results, we proposed a method for modeling the trade-off of privacy preservation and activity recognition on low-resolution images.