The graph of a logarithmic function passes through the point

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

The graph of a logarithmic function passes through the point (2,0)(2,0), has a vertical asymptote at x=1x=1, and is increasing on its domain. Which of the following could be its equation? (a) y=log⁡2(1−x)y=\log_{2}(1-x) (b) y=log⁡12(x−1)y=\log_{\tfrac12}(x-1) (c) y=log⁡2(x−1)y=\log_{2}(x-1) (d) y=log⁡2(x−1)+1y=\log_{2}(x-1)+1

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