91Ó°ÊÓ

Based on the step-by-step process of sketching the given logarithm functions, provide a short-answer explanation of the transformations that occur for each function: To sketch the graph for each given function, we apply specific transformations to the basic logarithm function \(y=\log_{2}x\): 1. \(y=\log_{2}(x-1)\): Apply a horizontal shift of 1 unit to the right. The vertical asymptote moves to \(x=1\) and the curve passes through \((2, 0)\). 2. \(y=\log_{2}x^2\): Replace \(x\) with \(x^2\), causing the graph to reflect about the y-axis, and becoming symmetric with respect to the y-axis. The curve still passes through \((1, 0)\). 3. \(y=(\log_{2}x)^2\): Square the basic logarithm function, which bends the curve upward with a gentle slope near the y-axis. The graph still passes through \((1, 0)\). 4. \(y=\log_{2}x+1\): Apply a vertical shift of 1 unit upwards. The vertical asymptote remains at \(x=0\) but the graph now passes through \((1, 1)\).