From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 12 Mar 2019 23:28:08 +0000 (+1100)
Subject: [methods] graphing exponential functions
X-Git-Tag: yr12~211
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/a83b38f59f0586a48c66b3e3a3d12a69de7543a9

[methods] graphing exponential functions
---

diff --git a/methods/stuff.md b/methods/stuff.md
index 661a69f..fb94066 100644
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -50,6 +50,7 @@ $\log_a(m^p) = p\log_am$
 $\log_a(m^{-1}) = -\log_am$  
 $\log_a1 = 0$ and $\log_aa = 1$
 
+
 ## Inverse functions
 
 Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$
@@ -72,3 +73,16 @@ $t$ is time taken
 $k$ is a constant  
 For continuous growth, $k > 0$  
 For continuous decay, $k < 0$
+m
+## Graphing expomnential functions
+
+$$f(x)=Aa^{k(x-b)} + c, \quad \vert a > 1$$
+
+- **$y$-intercept** at $(0, {{1+c} \over {a^b}})$
+- **horizontal asymptote** at $y=c$
+- **domain** is $\mathbb{R}$
+- **range** is $(c, \infty)$
+- dilation of factor $A$ from $x$-axis
+- dilation of factor $1 \over k$ from $y$-axis
+
+