Given the function;
[tex]h(x)=2|x-3|+1[/tex]A translation is a slide, which means that the function has the same shape graphically, but the graph of the function slides up or down or slides left or right to a different position on the coordinate plane.
Thus, when a function h(x) is translated c-units to the right, it becomes h(x-c).
Thus, the given function is translated 2 units to the right. We have;
[tex]\begin{gathered} h(x-2)=f(x)=2|x-2-3|+1 \\ f(x)=2|x-5|+1 \end{gathered}[/tex]