IB Maths AI 2.6 Notes

The base graph

A graph transformation changes the position, orientation or shape of a graph. Instead of drawing every new graph from scratch, it is usually easier to start from a known graph such as $y=f(x)$ and then apply the required transformation.

In this topic, you need to understand translations, reflections, stretches and composite transformations.

We begin with a known function $y=f(x)$. Every transformation compares the new graph to this original graph.

For example, if the base graph is $y=x^2$, then we can use transformations to sketch graphs such as $y=x^2+3$, $y=(x-2)^2$ or $y=-2x^2$.