2.8 Transformations of graphsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.8 Transformations of graphs

1. 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
2. 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
3. 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