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P12 June q2
4300
(a) Describe fully a sequence of two transformations which transforms the graph of \( y=f(x) \) to the graph of \( y=f(4-x) \).
(b) The curve with equation \( y=x^3-3x-4 \) is stretched with scale factor \( \frac12 \) in the \(x\)-direction and then translated by \( \begin{pmatrix}0\\-3\end{pmatrix} \).
Find and simplify the equation of the transformed curve.
Solution
✔ Checked by expert
(a) Since \( f(4-x)=f(-(x-4)) \), the graph may be transformed by:
reflection in the \(y\)-axis, followed by a translation \(4\) units in the positive \(x\)-direction.
(b) A stretch with scale factor \( \frac12 \) in the \(x\)-direction changes \(x\) to \(2x\):