MYP Extended Mathematics Function Transformations Key Definitions

A fixed point $C$ such that each point of the image lies on the line from $C$ through the original point, and its distance from $C$ is multiplied by the scale factor.

The transformation $y=f(ax)$, where $x$-values are scaled by a factor $\frac{1}{a}$. It is a dilation parallel to the $x$-axis.

A transformation that moves the graph of $y=f(x)$ left or right by changing the input to $f$.

The transformation $y=a f(x)$, where all $y$-values are multiplied by $a$. It is a dilation with scale factor $a$ parallel to the $y$-axis.

A transformation that adds a constant $k$ to a function so that every point moves up ($k>0$) or down ($k<0$) by the same number of units.