Question 4 - A-Level Maths

Identify the statement which is false. Find a counter example to show that this statement is in fact false.
Identify the statement which is true. Give a proof to show that this statement is in fact true. \item Figure 1 shows a sketch of the graph of \(y = f ( x )\). The graph has a minimum point at \(( - 3 , - 4 )\) and intersects the \(x\)-axis at the points \(( - 8,0 )\) and \(( 2,0 )\). \end{enumerate} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b1befa4f-5ef6-46e1-afb4-3a3582db7dfd-3_540_992_422_518} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure}
Sketch the graph of \(y = f ( x + 3 )\), indicating the coordinates of the stationary point and the coordinates of the points of intersection of the graph with the \(x\)-axis.
Figure 2 shows a sketch of the graph having one of the following equations with an appropriate value of either \(p , q\) or \(r\).
\(y = f ( p x )\), where \(p\) is a constant
\(y = f ( x ) + q\), where \(q\) is a constant
\(y = r f ( x )\), where \(r\) is a constant \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b1befa4f-5ef6-46e1-afb4-3a3582db7dfd-3_513_1072_1683_587} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Write down the equation of the graph sketched in Figure 2, together with the value of the corresponding constant.