Moderate -0.3 This is a standard C3 transformation question requiring application of two transformations: horizontal translation by -3 and vertical stretch with reflection by factor -4. Students must systematically apply transformations to given points, which is routine practice but requires careful execution of multiple steps without conceptual novelty.
2
\includegraphics[max width=\textwidth, alt={}, center]{774bb427-5392-45d3-8e4e-47d08fb8a792-02_538_1061_388_541}
The diagram shows the curve with equation \(y = \mathrm { f } ( x )\). It is given that \(\mathrm { f } ( - 7 ) = 0\) and that there are stationary points at \(( - 2 , - 6 )\) and \(( 0,0 )\). Sketch the curve with equation \(y = - 4 \mathrm { f } ( x + 3 )\), indicating the coordinates of the stationary points.
Draw graph showing reflection in a horizontal axis
M1
parallel to x-axis, in either direction; independent of first M1; not earned if curve still passes through \(O\) but ignore other coordinates given at this stage
Draw graph showing translation
M1
Draw (more or less) correct graph which must at least reach the negative x-axis, if not cross it, at left end of curve
A1
but ignoring no or wrong stretch in y-dir'n; condone graph existing only for \(x < 0\); consider shape of curve and ignore coordinates given
State \((-5, 24)\) and \((-3, 0)\) wherever located
B1
4 or clearly implied by sketch; allow for coordinates whatever sketch looks like; allow if in solution with no sketch
Draw graph showing reflection in a horizontal axis | M1 | parallel to x-axis, in either direction; independent of first M1; not earned if curve still passes through $O$ but ignore other coordinates given at this stage
Draw graph showing translation | M1 |
Draw (more or less) correct graph which must at least reach the negative x-axis, if not cross it, at left end of curve | A1 | but ignoring no or wrong stretch in y-dir'n; condone graph existing only for $x < 0$; consider shape of curve and ignore coordinates given
State $(-5, 24)$ and $(-3, 0)$ wherever located | B1 | 4 or clearly implied by sketch; allow for coordinates whatever sketch looks like; allow if in solution with no sketch
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2\\
\includegraphics[max width=\textwidth, alt={}, center]{774bb427-5392-45d3-8e4e-47d08fb8a792-02_538_1061_388_541}
The diagram shows the curve with equation $y = \mathrm { f } ( x )$. It is given that $\mathrm { f } ( - 7 ) = 0$ and that there are stationary points at $( - 2 , - 6 )$ and $( 0,0 )$. Sketch the curve with equation $y = - 4 \mathrm { f } ( x + 3 )$, indicating the coordinates of the stationary points.
\hfill \mbox{\textit{OCR C3 2011 Q2 [4]}}