We need to shift the extreme points of the original interval by 4 units to the right on the plane. By doing so, we will move the point x=-6 to x=-2 and x=3 to x=7.
Therefore, we need to shift the function f(x) 4 units to the right.
In general, given a function g(x), a translation to the right by c units is given by the transformation below
[tex]g(x)\to g(x-h)\text{ shift to the right by h units}[/tex]
In our problem, h=4 and f(x)=|x|; then,
[tex]f(x)=|x|\to g(x)=|x-4|[/tex]
The answer is option D, |x-4|
