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Single transformations mapping the natural logarithm graph onto related logarithmic graphs

Single transformations mapping the natural logarithm graph onto related logarithmic graphs

5 marks

For each of the following, describe a single transformation that maps the graph of \(y=\ln x\) onto the given graph.

  1. \(y=\ln\left(\frac1x\right)\)[1]
  2. \(y=\log_{\sqrt e}x\)[2]
  3. \(y=\ln\left(\frac x3\right)\), giving two different possible answers[2]

Solution:

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Answer:(a) reflection in the \(x\)-axis (b) stretch parallel to the \(y\)-axis, scale factor \(2\) (c) translation by \(\begin{pmatrix}0\\ -\ln3\end{pmatrix}\), or stretch parallel to the \(x\)-axis, scale factor \(3\)

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