| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, modulus involved) |
| Difficulty | Moderate -0.3 This is a straightforward function transformation question requiring students to apply standard rules: reflecting in y=x for inverse functions and applying a vertical stretch with reflection for -2f(x). While it requires careful attention to coordinate transformations, these are routine C3 techniques with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x) |
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The diagram shows the graph of $y = \mathrm { f } ( x )$. It is given that $\mathrm { f } ( - 3 ) = 0$ and $\mathrm { f } ( 0 ) = 2$. Sketch, on separate diagrams, the following graphs, indicating in each case the coordinates of the points where the graph crosses the axes:\\
(i) $y = \mathrm { f } ^ { - 1 } ( x )$,\\
(ii) $y = - 2 \mathrm { f } ( x )$.
\hfill \mbox{\textit{OCR C3 2008 Q2 [5]}}