Describe the transformations of the function f(x)=4/x-1-3

Assuming the parent function is p(x)=1/x.
then the transformation
q(x)=a/(x-h)+k
where
a=vertical stretch factor
h=horizontal shift
k=vertical shift
By matching with
f(x)=4/(x-1)-3
we have
a=4
h=1
k=-3
or
the transformations from parent function p=1/x are
scale factor for vertical stretch = 4
horizontal shift = 1 (i.e. to the right)
vertical shift = -3  (i.e. downwards)