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.
There are several terms that will be useful in describing functions. We first begin with the notion of an 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.
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.
A function \(f(x)\) is monotonic if it increases for all \(x\) or decreases for all \(x\text{.}\)
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.
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 \(k\text{.}\)