Hello
y=1/x is the classic hyperbola
y=1/(x-2)+3 can be derived from the classic one using a translation of vector 2i+3j
This is too vague and probably not the best way to explain this problem to the OP. Vectors are not necessary.
That is a good tool, but I suspect the OP needs to learn how to do this without a graphing aid.
-----------
Thank you for the help you two, just some stuff to think about is all.