IB Maths AI 2.6 Definitions

A transformation formed by applying more than one transformation to the same base graph, for example combining translations, reflections and stretches in a single function rule.

A stretch with scale factor between $0$ and $1$, which makes the graph closer to an axis; for example $y=pf(x)$ with $0\lt p\lt1$ compresses vertically and $y=f(qx)$ with $q\gt1$ compresses horizontally by scale factor $\frac{1}{q}$.

A transformation that multiplies the $x$-coordinate by a scale factor $k$ while leaving the $y$-coordinate unchanged, using $\begin{pmatrix}k&&0\\0&&1\end{pmatrix}$

A shift of $y=f(x)$ by $a$ units in the $x$-direction, given by $y=f(x-a)$.

A transformation that flips points in a line (such as an axis), reversing orientation while preserving distances.

The multiplicative factor that determines how much a graph is stretched or compressed, such as $p$ in $y=pf(x)$ for vertical scaling or $\frac{1}{q}$ in $y=f(qx)$ for horizontal scaling.

A movement of a graph that shifts every point the same distance without changing the shape of the graph.

A transformation that multiplies the $y$-coordinate by a scale factor $k$ while leaving the $x$-coordinate unchanged, using $\begin{pmatrix}1&&0\\0&&k\end{pmatrix}$

A shift of $y=f(x)$ by $b$ units in the $y$-direction, given by $y=f(x)+b$.