Moderate -0.8 This is a straightforward transformations question requiring students to identify that g(x) = 2f(x) - 1, corresponding to a vertical stretch by factor 2 followed by a translation down 1 unit. It tests basic understanding of function transformations with no problem-solving or novel insight required, making it easier than average but not trivial since students must correctly identify and order the transformations.
Given that \(\text{f}(x) = x^3\) and \(\text{g}(x) = 2x^3 - 1\), describe a sequence of two transformations which maps the curve \(y = \text{f}(x)\) onto the curve \(y = \text{g}(x)\). [4]
Question 2:
2 | [1-way] stretch
scale factor 2 in y-direction
e
translation
p
(cid:167) 0 (cid:183)
(cid:168) (cid:184)
(cid:169)(cid:16)1(cid:185) | M1
c A1
M1
A1
[4] | m
i1.1
1.1
1.1
1.1 | If transformations given in reverse
order then M1, A1, M1 are still
available (but not final A1)
Or −1 in y-direction
2 | 4 | 0 | 0 | 0 | 4 | 0
Given that $\text{f}(x) = x^3$ and $\text{g}(x) = 2x^3 - 1$, describe a sequence of two transformations which maps the curve $y = \text{f}(x)$ onto the curve $y = \text{g}(x)$. [4]
\hfill \mbox{\textit{OCR MEI Paper 2 Q2 [4]}}