Given $[a,b],[c,d] \subset \mathbb{R}$, we can take the natural bijection between those intervals
$$\phi: [a,b] \to [c,d] \\ x \mapsto (x-a) \frac{d-c}{b-a} + c$$
Does this bijection have any name?
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3It's can be dubbed the unique nondecreasing affine bijection between these intervals, but I doubt anyone has ever cared to giv a specific name to it. (Introducingthe name would take longer than thinking of the map) – Hagen von Eitzen Aug 07 '14 at 20:52
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How about "the linear map"? – MJD Aug 08 '14 at 02:02