Answer:
![y=|\frac{1}{4}x|](https://tex.z-dn.net/?f=y%3D%7C%5Cfrac%7B1%7D%7B4%7Dx%7C)
Step-by-step explanation:
Given that
transformed graph of the parent graph y=|x|
The transformed function is shown below:-
We see the graph at y=1 x reaches to 4 i.e, x=4
In the Same manner at y = 1
and x reaches to -4
that is
x=-4
Now, as per the options that are given in the question
The graph would be satisfied these two points would become transformation
![y=|\frac{1}{4}x|](https://tex.z-dn.net/?f=y%3D%7C%5Cfrac%7B1%7D%7B4%7Dx%7C)
Now,
At x=4
![y=|\frac{1}{4}x|](https://tex.z-dn.net/?f=y%3D%7C%5Cfrac%7B1%7D%7B4%7Dx%7C)
![y=|\frac{1}{4}(4)|](https://tex.z-dn.net/?f=y%3D%7C%5Cfrac%7B1%7D%7B4%7D%284%29%7C)
y = 1
we can say that the point totally satisfied the equation.
So, Option 1 is right that is
![y=|\frac{1}{4}x|](https://tex.z-dn.net/?f=y%3D%7C%5Cfrac%7B1%7D%7B4%7Dx%7C)
With the help of a diagram we can go through as attached.