2.8 Transformations of graphsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

The graph of y=f(x)+b compared with y=f(x)?
The graph of y=f(x-a) compared with y=f(x)?
What does the vector \begin{pmatrix}3\\ -2\end{pmatrix} mean?
y=-f(x) is which transformation?
y=f(-x) is which transformation?
y=p\,f(x) is which transformation?
y=f(qx) is which transformation?
Which points are invariant under a vertical stretch?
Why does the order of a composite transformation matter?
Transformations that map y=x^2 onto y=3x^2+2?
Transformations that map y=\sin x onto y=4\sin2x?
(4,6) is on y=f(x). Image on y=f(3x)?

Exam questions on 2.8 Transformations of graphs

The graph of $y=f(x)$ , where $f(x)=x^2+4$ , is translated by the vector $\begin{pmatrix}3\\ -2\end{pmatrix}$ to give the graph of $y=g(x)$ .
Find $g(x)$ in the form $ax^2+bx+c$ .2 marks
The point $P(4,6)$ lies on the graph of $y=f(x)$ .
The graph of $y=f(x)$ is stretched vertically with scale factor 3 and the resulting graph is then reflected in the $x$ -axis. Write down the equation of the final graph and the coordinates of the image of $P$ .2 marks
The graph of $y=\sin x$ ( $x$ in radians) is transformed to give the graph of $y=g(x)$ , where $g(x)=4\sin 2x+1$ .
Describe fully a sequence of three transformations that maps the graph of $y=\sin x$ onto the graph of $y=g(x)$ .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).