Edexcel C3 — Question 6

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
TopicCurve Sketching
TypeSketch multiple separate transformations

6. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{ddc10fc0-f3f2-4c5f-b152-eba68a21990f-08_871_1495_286_273}
\end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\). The curve has a minimum point at \(( - 0.5 , - 2 )\) and a maximum point at \(( 0.4 , - 4 )\). The lines \(x = 1\), the \(x\)-axis and the \(y\)-axis are asymptotes of the curve, as shown in Fig. 1. On a separate diagram sketch the graphs of
  1. \(y = | \mathrm { f } ( x ) |\),
  2. \(y = \mathrm { f } ( x - 3 )\),
  3. \(y = \mathrm { f } ( | x | )\). In each case show clearly
    1. the coordinates of any points at which the curve has a maximum or minimum point,
    2. how the curve approaches the asymptotes of the curve.
      6. continued