From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 7 Feb 2019 23:19:09 +0000 (+1100)
Subject: piecewise functions
X-Git-Tag: yr12~257
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/524700436a91433483a6c550a5b8ddcff6e55b48?ds=sidebyside

piecewise functions
---

diff --git a/methods/transformations.md b/methods/transformations.md
index 503257f..0a24a81 100644
--- a/methods/transformations.md
+++ b/methods/transformations.md
@@ -56,4 +56,24 @@ We can write $x^{-1 \over n} = {1 \over {x^{1 \over n}}} = {1 \over ^n \sqrt{x}}
 
 **Odd and even functions:**  
 Function is even if it can be reflected across $y$-axis $\implies f(x)=f(-x)$  
-If $n$ is odd, then $f$ is an odd function since $f(-x)=-f(x) \implies f(x)=-f(x)$
\ No newline at end of file
+If $n$ is odd, then $f$ is an odd function since $f(-x)=-f(x) \implies f(x)=-f(x)$
+
+## Combinations of functions (piecewise/hybrid)
+
+$$\text{e.g.}\quad f(x)=\begin{cases} ^3 \sqrt{x}, \hspace{2em} x \le 0 \\ 2, \hspace{3.4em} 0 < x < 2 \\ x, \hspace{3.4em} x \ge 2 \end{cases}$$
+
+Open circle - point included  
+Closed circle - point not included  
+
+### Sum, difference, product of functions
+| | | |
+|---|-----|-----|
+|sum|$f+g$|domain $= \text{dom}(f) \cap \text{dom}(g)$|
+|difference|$f-g$ or $g-f$|domain $=\text{dom}(f) \cap \text{dom}(g)$|
+|product|$f \times g$|domain $=\text{dom}(f) \cap \text{dom}(g)$|
+
+Addition of linear piecewise graphs - add $y$-values at key points
+
+Product functions:  
+- product will equal 0 if one of the functions is equal to 0
+- turning point on one function does not equate to turning point on product
\ No newline at end of file