Animals selecting habitats often have to consider many factors, e.g., food and cover for safety. However, each habitat type often lacks an adequate mixture of these factors. Analyses of habitat selection using resource selection functions (RSFs) for animal radiotelemetry data typically ignore trade‐offs, and the fact that these may change during an animal's daily foraging and resting rhythm on a short‐term basis. This may lead to changes in the relative use of habitat types if availability differs among individual home ranges, called functional responses in habitat selection. Here, we identify such functional responses and their underlying behavioral mechanisms by estimating RSFs through mixed‐effects logistic regression of telemetry data on 62 female red deer (Cervus elaphus) in Norway. Habitat selection changed with time of day and activity, suggesting a trade‐off in habitat selection related to forage quantity or quality vs. shelter. Red deer frequently used pastures offering abundant forage and little canopy cover during nighttime when actively foraging, while spending much of their time in forested habitats with less forage but more cover during daytime when they are more often inactive. Selection for pastures was higher when availability was low and decreased with increasing availability. Moreover, we show for the first time that in the real world with forest habitats also containing some forage, there was both increasing selection of pastures (i.e., not proportional use) and reduced time spent in pastures (i.e., not constant time use) with lowered availability of pastures within the home range. Our study demonstrates that landscape‐level habitat composition modifies the trade‐off between food and cover for large herbivorous mammals. Consequently, landscapes are likely to differ in their vulnerability to crop damage and threat to biodiversity from grazing.