Answer:
The represented function is :
![f(x)=(\frac{1}{4})^{x-2}](https://tex.z-dn.net/?f=f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bx-2%7D)
Step-by-step explanation:
![1.\thinspace f(x)=(\frac{1}{4})^x +2](https://tex.z-dn.net/?f=1.%5Cthinspace%20f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5Ex%20%2B2)
And the equation must pass through (2,1) as given,
But, f(2) = 2.0625 ≠ 1 so this is not the required function.
![2.\thinspace f(x)=(\frac{1}{4})^{x+2}](https://tex.z-dn.net/?f=2.%5Cthinspace%20f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bx%2B2%7D)
And the equation must pass through (2,1) as given,
But, f(2) = 0.0039 ≠ 1 so this is not the required function.
![3.\thinspace f(x)=(\frac{1}{4})^x -2](https://tex.z-dn.net/?f=3.%5Cthinspace%20f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5Ex%20-2)
And the equation must pass through (2,1) as given,
But, f(2) = -1.94 ≠ 1 so this is not the required function.
![4.\thinspace f(x)=(\frac{1}{4})^{x-2}](https://tex.z-dn.net/?f=4.%5Cthinspace%20f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bx-2%7D)
And the equation must pass through (2,1) as given,
We see, f(2) = 1 so this is the required function and the corresponding graph of the function is attached below :
Hence, The correct option is (4)