Answer:
All the options are incorrect.
Step-by-step explanation:
The parent absolute function is,
![f(x)=|x|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C)
An absolute function can be in the form of
![f(x)=a|x+b|+c](https://tex.z-dn.net/?f=f%28x%29%3Da%7Cx%2Bb%7C%2Bc)
Where a>1 shows vertical stretch and a<1 shows vertical compression. b>0 represents horizontal shift towards left and b<0 represents horizontal shift towards right. c>0 represent vertical shift in upward direction and c<0 represent vertical shift in downward direction.
The function in option 1 is,
![f(x)=|x|+3](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C%2B3)
It shows the vertical shift in upward direction by 3 units. Therefore option 1 is incorrect.
The function in option 2 is,
![f(x)=|x-6|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx-6%7C)
It shows the horizontal shift in right direction by 6 units. Therefore option 2 is incorrect.
The function in option 3 is,
![f(x)=|x|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C)
It is same as the parent function f(x). Therefore option 3 is incorrect.
The function in option 3 is,
![f(x)=9|x|](https://tex.z-dn.net/?f=f%28x%29%3D9%7Cx%7C)
It shows the vertical stretch therefore it will not wider than absolute parent function. Option 4 is incorrect.
The graph of f(x) is wider than the parent function if the function is in the form of
![f(x)=a|x|](https://tex.z-dn.net/?f=f%28x%29%3Da%7Cx%7C)
Where the value of a is lies between 1 to 1.
So option 3 is correct if the scale factor between 1 to 1 is omitted, otherwise all option are incorrect.