The figure below shows the sketch of the graph \(y=\mathrm{f}(x)\). The graph has asymptotes at \(x=1\), \(y=3\) and the \(x\)-axis. The graph has stationary point at \((-1,-3)\) and cuts the axes at \((0,0)\) and \((2,0)\).
Sketch, on separate diagrams, the following graphs, indicating clearly any asymptotes, axial intercepts and stationary points, where possible.
\(y=-2\mathrm{f}(x)+1\)[3]
\(y=\dfrac{1}{\mathrm{f}(x)}\)[3]
\(y=\mathrm{f}(|x|+1)\)[3]
Describe fully a sequence of transformations that transform the graph of \(y=x^2\) onto the graph of \(y=4x^2-4x+1\).[2]
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Answer:(b) stretch parallel to the \(x\)-axis by scale factor \(\dfrac12\), then translate by \(\begin{pmatrix}\frac12\\0\end{pmatrix}\)