Do you know how to scale the values in the range of $(-1, 1) $to the range of$ (0,30)$?

Question

I kind of forgot how to do this. Any help will be appreciated.

Answer 1

Try doing this in two steps:

1. First add $1$. This shifts the interval from $(-1,1)$ to $(0,2)$.
2. Now multiply by $15$. This stretches the interval $(0,2)$ to $(0,30)$.

Symbolically, if $x$ is in the interval $(-1,1)$ then computing $15(x+1)$ will yield a number in the interval $(0,30)$.

Answer 2

Consider a linear map that takes $-1$ to $0$, and $1$ to $30$. Then:

$0 = -1a + b$, and

$30 = 1a + b$.

So: $b = 15$, and $a = 15$. The transformation is:

$f(x) = 15x + 15$