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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 Function

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 $k\text{.}$