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Subsection1.8Describing Functions

There are several terms that will be useful in describing functions. We first begin with the notion of an increasing function.

Increasing Function

A function \(f\) is increasing if the values of \(f(x)\) increase as \(x\) increases. The graph of an increasing function climbs as we move from left to right.

Decreasing Function

A function \(f\) is decreasing if the values of \(f(x)\) decrease as \(x\) increases. The graph of a decreasing function falls as we move from left to right.

Monotonic Funcion

A function \(f(x)\) is monotonic if it increases for all \(x\) or decreases for all \(x\text{.}\)

Directly Proportional

We say \(y\) is directly proportional to \(x\) if there is a nonzero constant \(k\) such that, \(y = kx\text{.}\) This \(k\) is called the constant of proportionality.

Inversely Proportional

We say that \(y\) is inversely proportional to \(x\) if \(y\) is proportional to the reciprocal of \(x\text{,}\) that is, \(y = \frac{k}{x}\) for a nonzero constant \(k\text{.}\)