Transformations of graphsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

Effect of y=f(x)+a?
Effect of y=f(x+a)?
Effect of y=af(x) for a0?
Effect of y=f(ax) for a0?
Effect of y=-f(x)?
Under y=af(x), what happens to x-intercepts?
Under y=f(ax), what happens to the y-intercept?
A minimum is at (3,-2). Where is it on y=f(x)+4?
A minimum is at (3,-2). Where is it on y=f(x+4)?
A minimum is at (3,-2). Where is it on y=2f(x-1)?
Roots -2 and 3 on y=f(x). Roots of y=f(2x)?
What must you give to describe a stretch fully?

Exam questions on Transformations of graphs

The curve $y=f(x)$ has a minimum point at $(3,-2)$ .
Write down the coordinates of the minimum point of the curve $y=2f(x-1)$ .2 marks
The curve $y=f(x)$ crosses the $x$ -axis at $(-2,0)$ and $(3,0)$ only, and crosses the $y$ -axis at $(0,6)$ .
Describe fully the single transformation that maps $y=f(x)$ onto $y=f(x+2)$ , and write down the $x$ -intercepts of $y=f(x+2)$ .2 marks
The function $f$ is defined by $f(x)=x^2-4x+7$ .
Show that the curve $y=f(x+1)$ has equation $y=x^2-2x+4$ .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).