If a function f is increasing on an interval; if x1 < x2 then f(x1) < f(x2). What property is this?

• A. Non-decreasing
• B. Constant
• C. Monotonic decreasing
• D. Monotonic (strictly) increasing function

Answer: (D)

This describes how a function preserves order on an interval. If whenever you pick two inputs with x1 < x2 you always get outputs with f(x1) < f(x2), the function is strictly increasing on that interval. That is a stronger requirement than just increasing, which would allow f(x1) ≤ f(x2) and could include equal values for some x1 < x2. The term monotonic is about preserving order, and when the inequality is strict for all pairs, we call it monotonic (strictly) increasing. The other options don’t fit because non-decreasing allows equality, a constant function never increases, and monotonic decreasing would reverse the inequality. A simple example is f(x) = x, which is strictly increasing since larger inputs give strictly larger outputs.