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I have these values, all these values are in the range between $0$ and $1 (0, +1)$.

  • $0.3$
  • $0.5$
  • $0.8$
  • $0.9$

I want to change (translate) these values to a new range between $-1$ and $+1$ $(-1, +1)$, so I use the formula $y=2(x-0.5)$ (the magical number $2$ should expand the range to its extremes $(-1,+1)$ without disturbing the relations between the numbers):

  • $2 (0.3 - 0.5) = -0.4$
  • $2 (0.2 - 0.5) = -0.6$
  • $2 (0.8 - 0.5) = +0.6$
  • $2 (0.9 - 0.5) = +0.8$

Imagine I have other values from other ranges which I want to translate to the new domain $(-1,+1)$, so "$y=2(x-0.5)$" does not work for these ranges.

Are there any kind of (abstract) formula to make such translations?

nimo23
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1 Answers1

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For domain $(a,b)$, the formula is of the form of

$$y = p(x-m)$$

where $m =\frac{a+b}2$ and $p= \frac{1}{m-a}$.

Try to interpret the meaning of $m$ and $p$ for better understanding of the formula.

Exercise (to get another perspective):

  • Try to find the straight line that connects $(0,-1)$ to $(1,1)$.

  • Try to find the straight line that connects $(a,-1)$ to $(b,1)$.

Siong Thye Goh
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  • So I need "m" ? With x between (0,1), it is easy to know that m shold be "-0.5". What is m, if domain of x is (-999, +999) ? How can I translate this into new domain (-1, +1) ? – nimo23 Nov 17 '17 at 11:33
  • with $x$ between $(0,1), m$ should be $-0.5$?? check again? – Siong Thye Goh Nov 17 '17 at 11:36
  • When having x in range (0,1) and want to translate to (-1,1), then m must be "-0.5". The "2" is only a scaling factor which I want to have, so that the translated x-values are expanded to its range (-1,1). – nimo23 Nov 17 '17 at 11:40
  • Yup, that is correct. – Siong Thye Goh Nov 17 '17 at 11:41