From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Fri, 15 Mar 2019 03:53:04 +0000 (+1100)
Subject: [methods] graphing log functions
X-Git-Tag: yr12~204
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/b3dda2fb74ac506a0a2e33087d3b04bb66ea4bc8

[methods] graphing log functions
---

diff --git a/methods/stuff.md b/methods/stuff.md
index fb94066..bf8fbb0 100644
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -73,7 +73,7 @@ $t$ is time taken
 $k$ is a constant  
 For continuous growth, $k > 0$  
 For continuous decay, $k < 0$
-m
+
 ## Graphing expomnential functions
 
 $$f(x)=Aa^{k(x-b)} + c, \quad \vert a > 1$$
@@ -85,4 +85,17 @@ $$f(x)=Aa^{k(x-b)} + c, \quad \vert a > 1$$
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 
+## Graphing logarithmic functions
+
+$log_e x$ is the inverse of $e^x$ (reflection across $y=x$)
+
+$$f(x)=A \log_a k(x-b) + c$$
+
+where
+- **domain** is $(b, \infty)$
+- **range** is $\mathbb{R}^+$
+- **vertical asymptote** at $x=b$
+- $y$-intercept exists if $b<0$
+- dilation of factor $A$ from $x$-axis (reflection across $x$-axis when $A < 0$)  
+- dilation of factor $1 \over k$ from $y$-axis (reflection across $y$-axis when $k < 0$)