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1. Identifying the Equations of the Asymptotes For the function g(x) = 1/(x-1) 2, the asymptotes are lines the graph approaches but never touches. Vertical Asymptote: Set the denominator equal to zero: x - 1 = 0 → x = 1. This is the vertical asymptote. Horizontal Asymptote: Look at the constant added outside the fraction. As x approaches infinity, 1/(x-1) approaches 0, so g(x) approaches 2. The horizontal asymptote is y = 2. Pro Tip: Remember, asymptotes are the “boundaries” of the hyperbola! 2.
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