Question

Which function represents the graph of f(x)=|x+2| after it is translated 4 units to the right?

Answer 1

Answer:

$g(x)=|x-2|$

Step-by-step explanation:

The vertex form of an absolute function is

$g(x)=|x-h|+k$            .... (1)

where, (h,k) is vertex.

The given function is

$f(x)=|x+2|$

The vertex of the function is (-2,0).

It is given that graph of f(x) is translated 4 units to the right. So, the vertex of the function after translation is (2,0).

Substitute h=2 and k=0 in function (1).

$g(x)=|x-2|+0$

$g(x)=|x-2|$

Therefore, the required function is $g(x)=|x-2|$.