Here, the transformation $R$ is a reflection across the $x$-axis, while $T$ is a translation given by $\begin{pmatrix}3\\-1\end{pmatrix}$.
(a)[2]
Determine the equation, $y = g(x)$, for the curve $y = x^2$ once it has undergone the transformations $R$ followed by $T$.
(b)[2]
Determine the equation, $y = h(x)$, of the curve $y = x^2$ after the transformations have been carried out in the order $T$ and then $R$.
(c)[2]
State the transformation that takes the curve $y = g(x)$ to the curve $y = h(x)$, giving it in full.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resulting function $\{-(x-3)^2\}\{-1\}$” …
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