A function is monotone if it only increases or only decreases: f increases monotonically (is monotonic increasing) if x > y, implies thatf(x) ≥ f(y). A function f decreases monotonically (is monotonic decreasing) if x > y, implies thatf(x) ≤ f(y). A function f is strictly monotonically increasing if x > y, implies thatf(x) > f(y), and strictly monotonically decreasing if if x > y, implies thatf(x) < f(y).