Describe a linear function for which the least value in the range doesn't occur at the least value of the domain, that is the least value in the range isn't the initial value.

The domain of a function is your input or x and the range is the resulting y
If small values map to small values, then with growing input the result also grows or in other words the function has a positive slope.

The assignment wants you to find a linear function which does not do that, or in other words maps small x to large y and large x to small y. With growing x the y is therefore reduced and you have a negative slope. So the real question is "name any function with a negative slope". In this case with every step the range value gets smaller and so the first value can't be the least/smallest of the range.

so f(x)=-x would be solution

if you have to specify a domain and range you can pick something like D=[1,5] and R=[1,-5]

Iam unsure about what the proof is, therefore as much as wish to i can not.