Each of the graphs below is a transformation of the rational function $f(x) = \displaystyle \frac{1}{x}.$ Match the rational functions with one of the graphs.

 A B C D

 1 $f(x) = \frac{1}{x-1}+5$ 2 $f(x) = \frac{1}{x-1}$ 3 $f(x) = \frac{1}{x}+5$ 4 $f(x) = \frac{1}{x}+1$

Note: You can click on the graphs to enlarge the images.