Describe a sequence of two transformations that maps the graph of \(y=\ln \left( \frac{{{x}^{2}}}{x+

Question

Describe a sequence of two transformations that maps the graph of $y=\ln \left( \frac{{{x}^{2}}}{x+1} \right)$ onto the graph of $y=\ln \left( \frac{2x+1}{4{{x}^{2}}} \right)$.[2] The diagram below shows the graph of $y=\mathrm{f}\left( x \right)$. It has a maximum point at $A\left( -1,-1 \right)$ and a minimum point at $B\left( 1,\frac{1}{4} \right)$. The graph has asymptotes $y=\frac{1}{2}$, $x=0$ and $x=-2$. Sketch, on separate diagrams, the graphs of. $y=\mathrm{f}\left( 2-x \right)$,[2] $y=\frac{1}{\mathrm{f}\left( x \right)}$,[3] stating clearly the equations of any asymptotes, coordinates of any points of intersection with both axes and the points corresponding to $A$ and $B$.

Accepted Answer

(a) Scale $\times \dfrac{1}{2}$ in $x$, reflect in $x$-axis

2019 DHS P1 Q5

2019 DHS P1 Q5

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