Edexcel C3 — Question 4

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
TopicFunction Transformations
TypeMultiple separate transformations

4. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{909b52e5-2f16-4eab-b691-9d8fcf9bcfd9-3_604_1408_868_269}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x ) , - 1 \leq x \leq 3\). The curve touches the \(x\)-axis at the origin \(O\), crosses the \(x\)-axis at the point \(A ( 2,0 )\) and has a maximum at the point \(B \left( \frac { 4 } { 3 } , 1 \right)\). In separate diagrams, show a sketch of the curve with equation
  1. \(y = \mathrm { f } ( x + 1 )\),
  2. \(y = | \mathrm { f } ( x ) |\),
  3. \(y = \mathrm { f } ( | x | )\),
    marking on each sketch the coordinates of points at which the curve
    1. has a turning point,
    2. meets the \(x\)-axis.