Composite transformations of curvesAQA A-Level Further Maths: Mind map

Exam questions on Composite transformations of curves

1. The curve $C$ has equation $y=x^2+1$.
   The minimum point of $C$ is enlarged with scale factor 2, centre the origin, and its image is then translated by $\begin{pmatrix} 3 \\ -1 \end{pmatrix}$. Find the coordinates of the final position of the point.2 marks
2. The curve $C$ has equation $y=\mathrm{e}^x$.
   $C$ is rotated through $180^\circ$ about the origin and the image is then translated by $\begin{pmatrix} 0 \\ 3 \end{pmatrix}$. Find the equation of the final image and write down the equation of its asymptote.2 marks
3. The curve $C$ has equation $y=\dfrac{1}{x-2}$.
   $C$ is rotated through $90^\circ$ anticlockwise about the origin. Find the equation of the image, giving your answer in the form $y=\mathrm{g}(x)$.3 marks