To determine the range of the function y = 2x/(x - 1) through graphing, the function can be rewritten to identify its behavior. The transformation shows a horizontal asymptote at y = 2, indicating that the range excludes this value. Consequently, the range is defined as (-∞, 2) ∪ (2, ∞). The graph resembles y = 1/x, vertically stretched by a factor of 2 and shifted right and up, but these transformations do not change the overall range. Understanding these characteristics allows for accurate identification of the function's range.