Combined transformation sketches

Edexcel C3 2012 January Q2

\begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{363c5b5d-7ea9-41e5-ae5a-c3efb5626af5-03_716_1122_212_411} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} Figure 1 shows the graph of equation $y = \mathrm { f } ( x )$.
The points $P ( - 3,0 )$ and $Q ( 2 , - 4 )$ are stationary points on the graph.
Sketch, on separate diagrams, the graphs of

$y = 3 \mathrm { f } ( x + 2 )$
$y = | \mathrm { f } ( x ) |$ On each diagram, show the coordinates of any stationary points.

OCR C3 2011 January Q2

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.

Edexcel AEA 2005 June Q6

Find the coordinates of the points $P , Q$ and $R$.
Sketch, on separate diagrams, the graphs of
1. $y = \mathrm { f } ( 2 x )$,
2. $y = \mathrm { f } ( | x | + 1 )$,
  indicating on each sketch the coordinates of any maximum points and the intersections with the $x$-axis.
  (6) \begin{figure}[h]
  \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{f9d3e02c-cef2-435b-9cda-76c43fcac575-5_1015_1464_232_337}
  \end{figure} Figure 2 shows a sketch of part of the curve $C$, with equation $y = \mathrm { f } ( x - v ) + w$, where $v$ and $w$ are constants. The $x$-axis is a tangent to $C$ at the minimum point $T$, and $C$ intersects the $y$-axis at $S$. The line joining $S$ to the maximum point $U$ is parallel to the $x$-axis.
Find the value of $v$ and the value of $w$ and hence find the roots of the equation $$f ( x - v ) + w = 0$$