From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sun, 3 Feb 2019 23:40:47 +0000 (+1100)
Subject: methods transformations - f(x)
X-Git-Tag: yr12~266
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/6af190c2a952af72a71e7d83800023a8421f5130?ds=sidebyside

methods transformations - f(x)
---

diff --git a/methods/transformations.md b/methods/transformations.md
index 9a0b47b..ce58a10 100644
--- a/methods/transformations.md
+++ b/methods/transformations.md
@@ -1,5 +1,7 @@
 # Transformation
 
+**Order of operations:** DRT - Dilations, Reflections, Translations
+
 ## $f(x) = x^n$ to $f(x)=a(x-h)^n+K$##
 
 - $|a|$ is the dilation factor of $|a|$ units parallel to $y$-axis or from $x$-axis
@@ -24,4 +26,14 @@ For the graph of $y = f(x)$, there are two pairs of equivalent processes:
 2. - Dilating from $y$-axis: $(x, y) \rightarrow (ax, y)$
    - Replacing $x$ with $x \over a$ to obtain $y = f({x \over a})$
 
-For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.
\ No newline at end of file
+For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.
+
+## Transformations from $f(x)$ to $y=Af[n(x+c)]+b$#
+
+Applies to exponential, log, trig, power, polynomial functions.  
+Functions must be written in form $y=Af[n(x+c)] + b$
+
+$A$ - dilation by factor $A$ from $x$-axis (if $A<0$, reflection across $y$-axis)  
+$n$ - dilation by factor $1 \over n$ from $y$-axis (if $n<0$, reflection across $x$-axis)  
+$c$ - translation from $y$-axis ($x$-shift)  
+$b$ - translation from $x$-axis ($y$-shift)
\ No newline at end of file