13.3 Transformations of graphs — Practise

Work independently. Questions and answers are checked from the same problem bank. Questions marked H extend the Higher work.

1. H Translate $y=x^2$ up 4 units. Write its new equation.
2. H Translate $y=x^2$ 3 units right. Write its new equation.
3. H Translate $y=x^2$ 2 units left and 1 unit up. Give the equation and turning point.
4. H Reflect $y=x^3$ in the $x$-axis. Give the new equation.
5. H Reflect $y=x^2+1$ in the $y$-axis. Give the new equation.
6. H The point $(2,5)$ lies on $y=f(x)$. State its image after reflection in the $x$-axis.
7. H The point $(4,3)$ lies on $y=f(x)$. State its image after reflection in the $y$-axis.
8. H The point $(2,5)$ lies on $y=f(x)$. State its image under $y=f(x)-4$.
9. H H Starting with $y=f(x)$, reflect in the $x$-axis, then translate 3 units right and 2 units up. Write the transformed rule.