Single transformations of curvesAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

Effect of y=f(x)+a?
Effect of y=f(x-a)?
Effect of y=a\,f(x)?
Effect of y=f(ax)?
Effect of y=-f(x)?
Effect of y=f(-x)?
How do you reflect a curve in y=x?
How do you reflect a curve in y=-x?
Image of (a,b) under y=f\left(\frac x3\right)?
Image of (a,b) under y=2f(x)?
What must you state to describe a stretch fully?
What must you state to describe a translation fully?
Do asymptotes move under a transformation?

Exam questions on Single transformations of curves

The point $P(4,6)$ lies on the curve $y=\mathrm{f}(x)$ .
The curve $y=\mathrm{f}(x)$ is transformed to $y=\mathrm{f}(-x)$ . Find the coordinates of the image of $P$ and describe the transformation.2 marks
The curve $C$ has equation $y=x^2+2x$ .
$C$ is stretched parallel to the $x$ -axis with scale factor $2$ . Find the equation of the image.2 marks
The ellipse $E$ has equation $\dfrac{x^2}{4}+\dfrac{y^2}{9}=1$ .
$E$ is reflected in the line $y=x$ . Find the equation of the image, and the coordinates of the points where the image meets the $x$ -axis.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).