What is a relationship in which each input value corresponds to exactly one output value?

This type of relation is called a function (a simpler way to remember it is only one Y value for every X value).

In functions where there are turning points (local maxima or minima), different x-values will map onto the same y-value. However, if each x-value has exactly one y-value, then the function will either be increasing for all x ordecreasing for all x.

Such functions are called monotonic functions.