Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does it mean if a function is consistently increasing or decreasing?

1. It is a monotone function

2. It has more than one root

3. It will result in a vertical line

4. It cannot be graphed

The correct answer is: It is a monotone function

A function that is consistently increasing or consistently decreasing is referred to as a monotone function. This means that as the input values (or x-values) of the function increase, the output values (or y-values) either always increase or always decrease without any interruption. In practical terms, if you have a consistently increasing function, for any two points on the graph where the first point is to the left of the second, the y-value of the first point will always be less than that of the second. Similarly, for a consistently decreasing function, the y-value of the first point will always be greater than the second. This characteristic is crucial in mathematics, particularly in analysis, because it guarantees that the function does not have any local maxima or minima and provides clarity in understanding the behavior of the function over its domain. The other choices do not correctly describe the nature of consistently increasing or decreasing functions. A function having more than one root can be increasing or decreasing, but this trait alone doesn't define it as monotone. A function resulting in a vertical line is not a function in the traditional sense, as it fails the vertical line test. Lastly, all functions can be graphed, so the claim that a function cannot be graphed is incorrect. Therefore