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geometry: margin=2cm
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author: Andrew Lorimer
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- for $(ax)^n$, dilation factor is $1 \over a$ parallel to $x$-axis or from $y$-axis
- when $0 < |a| < 1$, graph becomes closer to axis
-## Translations
-
-For $y = f(x)$, these processes are equivalent:
-
-- applying the translation $(x, y) \rightarrow (x + h, y + k)$ to the graph of $y = f(x)$
-- replacing $x$ with $x − h$ and $y$ with $y − k$ to obtain $y − k = f (x − h)$
-
## Dilations
For the graph of $y = f(x)$, there are two pairs of equivalent processes:
For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.
+## Reflections
+
+- Reflection **in** axis = reflection **over** axis = reflection **across** axis
+- Translations do not change
+
+## Translations
+
+For $y = f(x)$, these processes are equivalent:
+
+- applying the translation $(x, y) \rightarrow (x + h, y + k)$ to the graph of $y = f(x)$
+- replacing $x$ with $x − h$ and $y$ with $y − k$ to obtain $y − k = f (x − h)$
+
## Transforming $f(x)$ to $y=Af[n(x+c)]+b$#
Applies to exponential, log, trig, power, polynomial functions.