From 091772f6b08fb79bbd9262f4eb435e4518cd57b6 Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 28 Mar 2019 21:50:39 +1100
Subject: [PATCH] [methods] minor methods updates from assignment 4

---
 methods/summary.md         |  2 +-
 methods/transformations.md | 20 +++++++++++++-------
 2 files changed, 14 insertions(+), 8 deletions(-)

diff --git a/methods/summary.md b/methods/summary.md
index 5cec66f..cc809d3 100644
--- a/methods/summary.md
+++ b/methods/summary.md
@@ -105,7 +105,7 @@ In general:
 ## Functions
 $$f:\operatorname{dom}(f) \rightarrow \mathbb{R},\quad f(x)=\dots$$
 - function - one $y$ (image) value per $x$ (preimage)
-- 1:1 function - unique $y$ for each $x$
+- 1:1 function - unique $y$ for each $x$ ($\sin x$ is not 1:1, $x^3$ is)
 
 **Domain $\operatorname{dom}(f)$:** set of all $x$ values in function
 - maximal (implied) domain - largest domain for which the rule is defined
diff --git a/methods/transformations.md b/methods/transformations.md
index 08ba312..153441b 100644
--- a/methods/transformations.md
+++ b/methods/transformations.md
@@ -1,5 +1,6 @@
 ---
 geometry: margin=2cm
+columns: 2
 author: Andrew Lorimer
 ---
 
@@ -16,13 +17,6 @@ author: Andrew Lorimer
 - 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:
@@ -35,6 +29,18 @@ 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.  
-- 
2.47.1