How to write a function for converting values ​​from one scale to another?

Question

Programming

There is a range of values ​​from 0.0 to 1.0, conditionally a basic scale of values ​​(subjectively, this is engine speed).
It is necessary to convert values ​​from this range to the values ​​of another scale, in which 2 values ​​are known, corresponding to the values ​​of the base scale 0.0, 0.2 and 1.0. We need a function that will allow us to calculate all intermediate values ​​of the new scale, from the known values ​​of the base scale. And values ​​of 0 of the base scale are always 0 of the final scale.
A linear function will do, and I assume that there will be 2 of them, under sections 0-0.2 and 0.2-1.0.
I hope I explained it clearly, an example:
there are values ​​of the final scale 0.0=0 (zeros are always equal for the scales), 0.2 = 1000 and 1.0 = 6000 . Bold marked the input values.

Answer 1

On the first interval
y=x*1000;
On the second
y=1000+(x-0.2)*(6000-1000)

Answer 2

Through 3 points you can draw a parabola, then you do not have to work with ranges.
Look at Lagrange interpolation for example.
https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D...
For your case Y =1250*X*(X+3.8)
X - This is the original
Y scale - This is the new scale
Y(0) = 0
Y(0.2) = 1000
Y(1) = 6000

Answer 3

This is called in school - to build the equation of a straight line from two points.