I'm coding a piece of software that has to deal with many quantities and mappings of these quantities to a this is "10 out of 100 bad" scale. For example: a server response time of 200ms is 50/100 bad. (i.e. the "severity score" of a 200ms response time is 50 on a scale from 0 to 100).
Here's another example, without loss of generality:
Suppose I have a "severity scale", that is (for example), a piecewise linear function from a measurable quantity (say, concentration of potassium in soil sample) to a value in the $[0,1]$ interval (representing a "severity score", "seriousness score", "economical threat score", etc).
Like this:
$$ f(v) = \begin{cases} 0.0 & \text{if $v$ is $60$ ppm or below}\\ 1.0 & \text{if $v$ is $100$ ppm } \\ 0.0 & \text{if $v$ is $170$ ppm or more} \\ \operatorname{lerp}(v, a, b) & \text{otherwise} \end{cases} $$
where $\operatorname{lerp}(v, a, b)$ is the linear interpolation of unknown $v$ from known $a$ and $b$, and $a$ and $b$ are the closest defined points that surround $v$. The domain of $v$ in this case is $[0, \infty]$, but let's pretend it's $[-\infty, +\infty]$, without loss of generality, just so the function definition makes sense for quantities that can be negative.
Informally, $f$ is a function representing a "scale" whose optimum is $100$ ppm, and both $60$ ppm and $170$ ppm are really bad. Values above 170 and below 60 are considered to be as bad as those extremes for the purposes of the scale.
My question: is there a name for such a mathematical scale? That is, a mapping from an unbounded quantity to a bounded interval?
EDIT: I think my soil example may have mislead some commenters. I don't mean to imply anything about the shape of the function with the example, only that it maps an arbitrary domain into the unit interval in someway.
