[methods] minor methods updates from assignment 4

diff --git a/methods/summary.md b/methods/summary.md
index 5cec66f564a1a8f7bfb192e9c12f707dc3e1faa6..cc809d35c0d3b3cc906604f020f5796be454fa99 100644 (file)
--- 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)
 ## 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
 
 **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 08ba3123d6c2e6fa91385082229dc569ff2b094a..153441bd9f0c3f9f72c42f0cf75421c7dbfad56a 100644 (file)
--- a/methods/transformations.md
+++ b/methods/transformations.md
@@ -1,5 +1,6 @@
 ---
 geometry: margin=2cm
 ---
 geometry: margin=2cm

+columns: 2

 author: Andrew Lorimer
 ---
 
 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
 
 - 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:
 ## 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.
 
 
 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.  
 ## Transforming $f(x)$ to $y=Af[n(x+c)]+b$#
 
 Applies to exponential, log, trig, power, polynomial functions.