Answer:
B.![F(x)=-\mid{x-1}\mid](https://tex.z-dn.net/?f=F%28x%29%3D-%5Cmid%7Bx-1%7D%5Cmid)
Step-by-step explanation:
We are given that a function
![f(x)=\mid x\mid](https://tex.z-dn.net/?f=f%28x%29%3D%5Cmid%20x%5Cmid)
We have to find absolute value of function when parent function reflected over the x- axis and translated 1 unit to the right.
The transformation rule when the point (x,y) is reflected over x- axis is given by
![(x,y)\rightarrow (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28x%2C-y%29)
Apply the reflection on function over x- axis then, we get
![g(x)=-\mid x\mid](https://tex.z-dn.net/?f=g%28x%29%3D-%5Cmid%20x%5Cmid)
Transformation rule when the point (x,y) is shifted a units towards right is given by
![(x,y)\rightarrow (x-a,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28x-a%2Cy%29)
When the graph is translated 1 units towards right then , obtained function is given by
![F(x)=-\mid{x-1}\mid](https://tex.z-dn.net/?f=F%28x%29%3D-%5Cmid%7Bx-1%7D%5Cmid)