The docking sequence can start when the craft is within 10km, but that fact isn't related to the function at all. The function just tells how long it takes for the space craft to be a certain distance from the space station. The domain is then 0<d<= 1000 because the function begins to work when the space craft is 1000km away, and it obviously stops working when the distance between the spacecraft and station is 0m.The domain is supposed to be 0<d< or = 1000

but why isn't it 10<d< or = 1000

Doesnt it say in the question that "the docking sequence can be initialized once the craft is within 10 km of the station's docking bay", hence the 10 and not 0 in the domain?????

Or think of it like this: the spacecraft is still moving toward the space station while it is docking. The spacecraft only stops when it hits the space station (0 km away).