Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What describes a monotone function?

1. A function that is always increasing or always decreasing

2. A function that is constant throughout its domain

3. A function that has both increasing and decreasing intervals

4. A function that intersects the x-axis multiple times

The correct answer is: A function that is always increasing or always decreasing

A monotone function is characterized by its behavior of consistently moving in one direction across its entire domain, which means it is always increasing or always decreasing. This definition captures two specific types of monotonic functions: monotonic increasing functions, where the values never decrease as the input increases, and monotonic decreasing functions, where the values never increase as the input increases. For example, if you take a function that steadily rises from left to right without any dips or flat sections, this is a monotonic increasing function. Likewise, if a function consistently drops as you move along the x-axis, it is classified as a monotonic decreasing function. The other descriptions do not align with the definition of a monotone function. A function that is constant throughout its domain does not fit since it is not increasing or decreasing; it remains unchanged. A function with both increasing and decreasing intervals cannot be deemed monotonic because it fails to maintain a consistent direction. Finally, a function that intersects the x-axis multiple times may have various behaviors that do not imply monotonicity, as it could both increase and decrease between intersections. Thus, the key aspect of a monotone function is its unwavering tendency to move in a single direction.