Given the function:
[tex]F(x)=|x|[/tex]
And the function:
[tex]G(x)[/tex]
You know that they have the same shape.
According to the Transformation Rules for Functions, when:
[tex]f(x)-k[/tex]
The function is shifted down "k" units.
In this case, you can identify that the function G(x) was obtained by shifting the other function 5 units down. Therefore, knowing that:
[tex]k=5[/tex]
You can determine that its equation is:
[tex]G(x)=|x|-5[/tex]
Hence, the answer is: Option A.
