Answer:
(i)
![f(x)=-|x|](https://tex.z-dn.net/?f=f%28x%29%3D-%7Cx%7C)
(ii)
![f(x)=-|x-1|](https://tex.z-dn.net/?f=f%28x%29%3D-%7Cx-1%7C)
Step-by-step explanation:
we are given two different questions
(i)
parent function is
![f(x)=|x|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C)
now, it is reflected over x-axis
Suppose, (x,y) is reflected over x-axis
(x,y) becomes (x,-y)
So, we replace y as -y and x remain same
so, we get
![-f(x)=|x|](https://tex.z-dn.net/?f=-f%28x%29%3D%7Cx%7C)
So, our required function is
![f(x)=-|x|](https://tex.z-dn.net/?f=f%28x%29%3D-%7Cx%7C)
(ii)
parent function is
![f(x)=|x|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C)
now, it is reflected over x-axis
Suppose, (x,y) is reflected over x-axis
(x,y) becomes (x,-y)
So, we replace y as -y and x remain same
so, we get
![-f(x)=|x|](https://tex.z-dn.net/?f=-f%28x%29%3D%7Cx%7C)
![f(x)=-|x|](https://tex.z-dn.net/?f=f%28x%29%3D-%7Cx%7C)
now, it is translated 1 unit to right side
Whenever any function is translated to right side by 'a' units
so, we can replace x as x-a
so, we can replace x as x-1 here
we get
![f(x)=-|x-1|](https://tex.z-dn.net/?f=f%28x%29%3D-%7Cx-1%7C)