Understanding the resource needs of animals is critical to their management and conservation. Resource utilization functions (RUFs) provide a framework to investigate animal-resource relationships by characterizing variation in the amount of resource use. In this context a ‘resource’ is any aspect of a species' fundamental niche that can be mapped throughout the area of investigation (such as study area or home range). Extensive global positioning system (GPS) data from 17 cougars (Puma concolor) demonstrate the utility and potential challenges of estimating RUFs within the home range for far-ranging species. Ninety-nine per cent utilization distributions (UDs) estimated using bivariate plug in, univariate least-squares cross-validation and reference bandwidth selection methods were compared. Distance to water, per cent clear-cut and regenerating forest, and slope were used to estimate cougar RUFs. UDs derived from GPS data were more refined, and plug-in UDs were least similar to UDs derived from other bandwidths. RUFs were resilient to variation in the smoothing parameter, with all methods yielding coefficients that largely reflected observations of foraging ecology and behaviour. Cougars were individualistic, but use was generally positively associated with the presence of regenerating forest and inversely associated with steep slopes. Advances in technology allow for greater accuracy and resolution of the UD, but software improvements and spatially explicit information on animal behaviour are needed to better understand resource use.