Algebra-2

A. y = 1 /(x-1) + 3:
This function matches the given graph, as it compare to the parent function y = 1/x, shifted rightward by 1 unit, compressing it vertically around the vertical asymptote x = 1, and shifting it upward by 3 units.

B. y = 1 /(x+1) + 3:
This function does not match the given graph because it has a different horizontal shift. The horizontal shift is -1 instead of -1.