Answer:
y = 1/(x -2) +1
Explanation:
You want the equation and graph of y = 1/x after it has been shifted right 2 units and up 1 unit.
Translation
The graph of a function is translated right h units and up k units by ...
g(x) = f(x -h) +k
You want the function f(x) = 1/x translated with (h, k) = (2, 1). That will be ...
g(x) = f(x -2) +1
Your equation is ...
y = 1/(x -2) +1
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Additional comment
If you like, you can simplify this to ...
y = (x -1)/(x -2)
The shifted graph is shown in blue. The asymptotes of the original are the axes. The asymptotes of the shifted function are the dashed orange lines.
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