Scaling of basis hat functions to given domain

Question

I would like to transform the standard function values of the hat functions from $[0,1]$ to a given domain $[-R,R]$, whereas the standard hat functions are given through:

$\begin{align} \varphi(x) = \max\{1-|x|,0\} \end{align} $

I am not able to find that out. I also made a small illustration:

Answer 1

Am I correct that

$\begin{align} \psi(x) = \varphi\left( \frac{x - R}{2R}\right) \end{align}$

seems like the solution.