Answer: I think it is f(x)=1/(x-4)
Explanation:
By taking f(x), and applying a left or right and/or up or down transformations to it, the function could be written using the equation f(x-h)+k.
Doing so will make the graph of the function move h units to the left or right. (Positive or negative) (make sure the operation before the h is subtraction when determining the sign of h)
Also, when finding k (up and down) (positive or negative) apply this function.
f(x)=(x-h)+k
As a result, plug in your right 4 units as h, and since you are not needing to move up or down k would be 0. So, f(x)=1/(x-(4))+0 or simplified, f(x)=1/(x-4)