True or false: There exists a monotonic function f: R → R whose range is the set of integers. True False

A function that is [Select] interval [a, b] has [Select] on a [Select] on that interval.

(6a)  how many different functions f : A → B can be defined if m=3 and n=5?  (6b) if m=4 and n=6 then how many different one-to-one functions f : A →B can be defined? (6c) if m=5 and n=4 then how many different onto functions f : A → B can be defined?

Prove : if f is strictly monotone on its domain then f is one to one function