Answer:
[tex]g(x)=-|x-2|[/tex]
Step-by-step explanation:
Let as assume we need to find the function, when the parent absolute value function is reflected across the x-axis and translated right 2 units.
The parent absolute value function is
[tex]f(x)=|x|[/tex]
If the function f(x) is reflected over the x-axis, then f(x) will become -g(x). The function will become:
[tex]-g(x)=f(x)[/tex]
[tex]g(x)=-f(x)[/tex]
[tex]g(x)=-|x|[/tex]
After that, the function is translated 2 unit to the right.
[tex](x,y)\rightarrow (x+2,y)[/tex]
[tex]x'=x+2[/tex]
[tex]x'-2=x[/tex]
Substitute (x-2) for x, to find the new function.
[tex]g(x)=-|x-2|[/tex]
Therefore, the required function is [tex]g(x)=-|x-2|[/tex].
