Composite transformations of curvesAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

Image of y=f(x) under a 180^\circ rotation about the origin?
Image of y=f(x) under a 90^\circ anticlockwise rotation about the origin?
Image of y=f(x) under a 90^\circ clockwise rotation about the origin?
Map for a 90^\circ anticlockwise rotation about the origin?
Image of y=f(x) under an enlargement, scale factor k, centre the origin?
Which rotation equals an enlargement with scale factor -1?
What does y=f(x+a) do to the curve?
What does y=f(ax) do to the curve?
What does 'A followed by B' mean?
Why does the order matter for a translation and an enlargement?
How can you check an image equation quickly?
Where does the point (a,b) go under a 180^\circ rotation about the origin?

Exam questions on Composite transformations of curves

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).