f(x)=e^x 1 unit to the left, you’re left with g(x)=e^(x+1) (Fig. A). This transformation is pretty simple; the new line is 1 unit away. However, it’s only 1 unit away horizontally. Vertically, it varies depending on the x value. The vertical difference at x=-1 is a lot smaller than the vertical difference at x=1.
On this recent #hack-night, @carrot and I set out to transform f(x) so that at any point along f(x), the distance to the closest point on g(x) is equal to 1. Essentially, g(x) is 1 unit away throughout, not horizontally (Fig. B).
This proved to be quite difficult. There were a lot of quadratics that needed solving, and we also had to use the pythagorean theorem to get some distances. He can probably explain the math behind it a lot better than I can.
Anyways, here are a few links if you want to try it out:
• Exponential Functions - www.desmos.com/calculator/euke7u53si
• Quadratic Functions - www.desmos.com/calculator/jekjpm1mj0
• Linear Functions - www.desmos.com/calculator/oljptwxhji
• Circles - www.desmos.com/calculator/uedqiqjjxk (I think)
