For monotonic functions in one variable, the range of values is simple to compute. If f: \R \to \R is monotonically increasing (resp. decreasing) in the interval [x_1, x_2], then for all y_1, y_2 \in [x_1, x_2] such that y_1 \leq y_2, f(y_1) (resp. f(y_2) < f(y_1)).
