Single transformations of curvesAQA A-Level Further Maths: Mind map

Exam questions on Single transformations of curves

1. The point $P(4,6)$ lies on the curve $y=\mathrm{f}(x)$.
   The curve $y=\mathrm{f}(x)$ is transformed to $y=\mathrm{f}(-x)$. Find the coordinates of the image of $P$ and describe the transformation.2 marks
2. The curve $C$ has equation $y=x^2+2x$.
   $C$ is stretched parallel to the $x$-axis with scale factor $2$. Find the equation of the image.2 marks
3. The ellipse $E$ has equation $\dfrac{x^2}{4}+\dfrac{y^2}{9}=1$.
   $E$ is reflected in the line $y=x$. Find the equation of the image, and the coordinates of the points where the image meets the $x$-axis.3 marks