ANSWER and EXPLANATION
We want to identify the transformations that were made in obtaining:
[tex]g(x)=-|x-4|-2[/tex]from:
[tex]f(x)=|x|[/tex]When a function is transformed by:
[tex]g(x)\to-f(x)[/tex]It implies that there is a reflection across the x-axis.
When a function is transformed by:
[tex]g(x)\to f(x)-k[/tex]It implies that there is a vertical shift downwards by k units.
When a function is transformed by:
[tex]g(x)\to f(x-h)[/tex]it implies that there is a horizontal shift to the right by h units.
Therefore, for the given function, the transformations made are:
* Vertical shift
* Horizontal shift
* Reflection about the x-axis.