How do cheetahs react to environmental change?
The same as any mammal - they would need to move to a habitat to which they have evolved in to thrive and survive..
Cheetahs as a large carnivore are dependent on where there prey is and consequently, if the environment of their prey changes, their prey will try to move to the same ecosystem and climate that they evolved in - so, the cheetah would have to follow their prey. Cheetahs and their prey have co-evolved together over millions of years and their fates are interlinked when the climate or environment changes.
To some extent this happens on an annual basis in east Africa. As the rains come to the savannah, the plants green-up and the herbivores follow the grass. In turn, the carnivores like cheetahs follow the herbivores. As the rainfall moves northward with the changing seasons, the grass moves north and so then to the herbivores and carnivores.