6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{52f73407-14c5-46e6-b911-aa096b9b5893-10_781_858_239_575}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve with the equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\). The curve has a turning point at \(A ( 3 , - 4 )\) and also passes through the point \(( 0,5 )\).
- Write down the coordinates of the point to which \(A\) is transformed on the curve with equation
- \(y = | \mathrm { f } ( x ) |\),
- \(y = 2 f \left( \frac { 1 } { 2 } x \right)\).
- Sketch the curve with equation
$$y = \mathrm { f } ( | x | )$$
On your sketch show the coordinates of all turning points and the coordinates of the point at which the curve cuts the \(y\)-axis.
The curve with equation \(y = \mathrm { f } ( x )\) is a translation of the curve with equation \(y = x ^ { 2 }\).
- Find \(\mathrm { f } ( x )\).
- Explain why the function f does not have an inverse.