I have an alpha value with a range of 0.0 - 1.0 as well as a value N. If the alpha value is 0.5, I want to make no change to N. If the alpha value is 0, I want to double N. If the alpha value is 1.0 I want to halve N.
I want a clean formula to represent these values as well as all values in between. 0.25 should be 1.5N, and 0.75 should be 0.75N.
It seems really simple, but I'm having difficult wrapping my head around it for some reason.
From the data:
$x$-axis is $\alpha$ and $y$-axis is the multiplier of $N$.
Result: $$N\left(0.5|x-0.5|-1.5x+1.75\right).$$