Question

The function f (x)= |x| is graphed with a domain of [-6, 3). Which translation of the graph has the domain [-2,7]?

Answer 1

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

`g(x)\to g(x-h)\text{ shift to the right by h units}`

In our problem, h=4 and f(x)=|x|; then,

`f(x)=|x|\to g(x)=|x-4|`

The answer is option D, |x-4|