Combining graph transformationsEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

What does y=f(x)+a do?
What does y=f(x+a) do?
What does y=af(x) do?
What does y=f(ax) do?
What does y=-f(x) do?
What does y=f(-x) do?
Where does (p,q) go under y=2f(3x)?
Where does (p,q) go under y=f(-x)+1?
Which transformations are 'inside the brackets'?
How is y=3+\sin2x formed from y=\sin x?
Range of y=3+\sin2x?
Describe y=-\cos\left(x+\frac{\pi}{4}\right) from y=\cos x.
Is y=f(ax+b) required?

Exam questions on Combining graph transformations

The curve $y=f(x)$ has a maximum point at $(2,5)$ and crosses the $y$ -axis at $(0,1)$ .
Find the coordinates of the turning point of the curve $y=3-f\left(\frac{x}{2}\right)$ and state whether it is a maximum or minimum.2 marks
The point $A(4,-6)$ lies on the curve $y=f(x)$ .
Write down the coordinates of the image of $A$ on the curve $y=-f(-x)$ .2 marks
The function $g$ is defined by $g(x)=3+\sin2x$ for $0\leqslant x\leqslant2\pi$ , where $x$ is in radians. It is formed by transforming $y=\sin x$ .
Describe the sequence of transformations that maps $y=\sin x$ to $y=g(x)$ , and state the period of $g$ .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).