1# Transformation 2 3## $f(x) = x^n$ to $f(x)=a(x-h)^n+K$## 4 5- $|a|$ is the dilation factor of $|a|$ units parallel to $y$-axis or from $x$-axis 6- if $a<0$, graph is reflected over $x$-axis 7- $k$ - translation of $k$ units parallel to $y$-axis or from $x$-axis 8- $h$ - translation of $h$ units parallel to $x$-axis or from $y$-axis 9 10## Translations 11 12For $y = f(x)$, these processes are equivalent: 13 14- applying the translation $(x, y) \rightarrow (x + h, y + k)$ to the graph of $y = f$(x)$ 15- replacing $x$ with $x − h$ and $y$ with $y − k$ to obtain $y − k = f (x − h)$ 16 17## Dilations 18 19For the graph of $y = f(x)$, there are two pairs of equivalent processes: 20 211. - Dilating from $x$-axis: $(x, y) \rightarrow (x, by)$ 22 - Replacing $y$ with $y \over b$ to obtain $y = b f(x)$ 23 242. - Dilating from $y$-axis: $(x, y) \rightarrow (ax, y)$ 25 - Replacing $x$ with $x \over a$ to obtain $y = f({x \over a})$ 26 27For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.