Question

The parent absolute value function is reflected across the x-axis and translated right 2 units.

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Answer 1

f(x) = |x|

g(x) = -|x - 2|

Answer 2

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

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

`f(x)=|x|`

If the function f(x) is reflected over the x-axis, then f(x) will become -g(x). The function will become:

`-g(x)=f(x)`

`g(x)=-f(x)`

`g(x)=-|x|`

After that, the function is translated 2 unit to the right.

`(x,y)\rightarrow (x+2,y)`

`x'=x+2`

`x'-2=x`

Substitute (x-2) for x, to find the new function.

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

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