Combining graph transformationsEdexcel International A Level Maths: Mind map

Exam questions on Combining graph transformations

1. 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
2. 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
3. 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