A monotone function is one that constantly increases or decreases. Which description is correct?

A monotone function is one that constantly increases or decreases. Which description is correct?

• A. The graph increases and decreases.
• B. The graph is constant.
• C. The graph is strictly increasing or strictly decreasing across its entire domain.
• D. The graph has a horizontal tangent everywhere.

Answer: (C)

A monotone function moves in one direction across its entire domain. That means for any two inputs with x1 < x2, the outputs must either always increase (f(x1) < f(x2)) or always decrease (f(x1) > f(x2)) as you move along the domain. When this happens everywhere, the function is strictly increasing or strictly decreasing throughout its domain. This is exactly what the statement describes. If you allowed any flat parts where the value doesn’t change, you’d have a non-decreasing (or non-increasing) function, not strictly monotone. The other options either suggest the function changes direction, is constant, or imply a horizontal tangent everywhere, which does not capture the idea of moving consistently in one direction across the whole domain. So the description that fits monotone behavior in the strict sense is the function being strictly increasing or strictly decreasing across its entire domain.

A monotone function moves in one direction across its entire domain. That means for any two inputs with x1 < x2, the outputs must either always increase (f(x1) < f(x2)) or always decrease (f(x1) > f(x2)) as you move along the domain. When this happens everywhere, the function is strictly increasing or strictly decreasing throughout its domain. This is exactly what the statement describes.

If you allowed any flat parts where the value doesn’t change, you’d have a non-decreasing (or non-increasing) function, not strictly monotone. The other options either suggest the function changes direction, is constant, or imply a horizontal tangent everywhere, which does not capture the idea of moving consistently in one direction across the whole domain. So the description that fits monotone behavior in the strict sense is the function being strictly increasing or strictly decreasing across its entire domain.