Combinations of transformationsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

Image of (x,y) under y=af(x+b)+c?
In y=af(x)+c, which comes first: stretch or translation?
Which part of y=af(x+b)+c changes x-coordinates?
Rewrite f(2x-4) to show the translation.
A minimum is at (1,-3). Where is it on y=2f(x)+1?
A minimum is at (1,-3). Where is it on y=f(2x-4)?
A minimum is at (1,-3). What is the turning point of y=3-f(x)?
What transformation does -f(x) include?
How do you describe y=2(x-3)^2+1 from y=x^2?
Minimum point of y=2(x-3)^2+1?
A maximum (-2,5) becomes what under y=g(x+3)-2?
How can you find unknowns a, b, c in y=af(x+b)+c?

Exam questions on Combinations of transformations

The curve $y=f(x)$ has a minimum point at $(1,-3)$ .
Write down the coordinates of the turning point of the curve $y=3-f(x)$ and state whether it is a maximum or a minimum.2 marks
The curve $y=g(x)$ has a maximum point at $(-2,5)$ and crosses the $x$ -axis at $(-5,0)$ and $(1,0)$ .
Write down the coordinates of the maximum point of the curve $y=2g(x-1)-3$ .2 marks
The curve $C$ has equation $y=x^2$ . The curve $D$ has equation $y=2(x-3)^2+1$ .
Describe a sequence of three transformations that maps $C$ onto $D$ .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).