Standard +0.3 This question requires systematic application of three transformations in sequence, which is more involved than single transformations but follows standard rules. The algebraic manipulation is straightforward once the transformation rules are applied correctly. It's slightly above average difficulty due to the sequential nature and potential for errors in ordering, but remains a routine exercise for students who know the transformation rules.
2 A function f is defined by \(\mathrm { f } ( x ) = x ^ { 2 } - 2 x + 5\) for \(x \in \mathbb { R }\). A sequence of transformations is applied in the following order to the graph of \(y = \mathrm { f } ( x )\) to give the graph of \(y = \mathrm { g } ( x )\).
Stretch parallel to the \(x\)-axis with scale factor \(\frac { 1 } { 2 }\)
Reflection in the \(y\)-axis
Stretch parallel to the \(y\)-axis with scale factor 3
Find \(\mathrm { g } ( x )\), giving your answer in the form \(a x ^ { 2 } + b x + c\), where \(a , b\) and \(c\) are constants.
2 A function f is defined by $\mathrm { f } ( x ) = x ^ { 2 } - 2 x + 5$ for $x \in \mathbb { R }$. A sequence of transformations is applied in the following order to the graph of $y = \mathrm { f } ( x )$ to give the graph of $y = \mathrm { g } ( x )$.
Stretch parallel to the $x$-axis with scale factor $\frac { 1 } { 2 }$\\
Reflection in the $y$-axis\\
Stretch parallel to the $y$-axis with scale factor 3\\
Find $\mathrm { g } ( x )$, giving your answer in the form $a x ^ { 2 } + b x + c$, where $a , b$ and $c$ are constants.\\
\hfill \mbox{\textit{CAIE P1 2023 Q2 [4]}}