Edexcel C12 2017 June — Question 7

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2017
SessionJune
TopicCurve Sketching
TypeSketch transformed curve from description

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08b1be3e-2d9a-4832-b230-d5519540f494-20_588_839_219_550} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\). The curve crosses the \(y\)-axis at the point \(( 0,8 )\). The line with equation \(y = 10\) is the only asymptote to the curve.
The curve has a single turning point, a minimum point at \(( 2,5 )\), as shown in Figure 3.
  1. State the coordinates of the minimum point of the curve with equation \(y = \mathrm { f } \left( \frac { 1 } { 4 } x \right)\)
  2. State the equation of the asymptote to the curve with equation \(y = \mathrm { f } ( x ) - 3\) The curve with equation \(y = \mathrm { f } ( x )\) meets the line with equation \(y = k\), where \(k\) is a constant, at two distinct points.
  3. State the set of possible values for \(k\).
  4. Sketch the curve with equation \(y = - \mathrm { f } ( x )\). On your sketch, show clearly the coordinates of the turning point, the coordinates of the intersection with the \(y\)-axis and the equation of the asymptote. \section*{\textbackslash section*\{D\}}