TITLE: Going from a value inside $[-1,1]$ to a value in another range
QUESTION [19 upvotes]: How does one calculate the value within range $-1.0$ to $1.0$ to be a number within the range of e.g. $0$ to $200$, or $0$ to $100$ etc. ?

REPLY [9 votes]: A short proof of Matt L.'s answer:
We want a function $f: [a, b] \rightarrow [c, d]$ such that
$$
\begin{alignat}{2}
f&(&a) &= c \\
f&(&b) &= d.
\end{alignat}
$$
If we assume the function is to be linear (that is, the output scales as the input does), then
$$\dfrac{d - c}{b - a} = \dfrac{f(x) - f(a)}{x - a}.$$
Simplifying yields the desired formula for $y = f(x)$.