Hard +2.5 This question requires students to work backwards from a composition of transformations, recognizing that ln x and e^(3x) - 5 are inverse-related functions, then decomposing the transformation into reflection in y=x, horizontal scaling by factor 1/3, and vertical translation by -5. This demands deep understanding of function transformations and inverse relationships rather than routine application, making it significantly harder than typical A-level questions.
Accept '5 units in the negative y-direction' or '−5 units parallel to the y-axis'; Do not accept 'in/on/across/up the y-axis'
Order of transformations must be correct for all 4 marks to be awarded
Reflection, stretch and translation | B1 | All three correct; Do not accept any other wording
(reflection) in the line $y = x$ | B1 |
(stretch) scale factor $\frac{1}{4}$ parallel to the x-axis | B1 | Accept 'in the x-direction'; accept 'factor' or 'SF' for 'scale factor'; Do not accept 'in/on/across/up the x-axis' or '$\frac{1}{4}$ units'
(translation) $\begin{pmatrix}0\\-5\end{pmatrix}$ | B1 | Accept '5 units in the negative y-direction' or '−5 units parallel to the y-axis'; Do not accept 'in/on/across/up the y-axis'
Order of transformations must be correct for all 4 marks to be awarded | |
A sequence of three transformations maps the curve $y = \ln x$ to the curve $y = \mathrm{e}^{3x} - 5$. Give details of these transformations. [4]
\hfill \mbox{\textit{OCR H240/03 2018 Q3 [4]}}