[methods] graphing exponential functions

diff --git a/methods/stuff.md b/methods/stuff.md
index 661a69f0ba46b88e71b1d8233bb8110fd71f980e..fb94066fe41f81f2354aa5c6747d75205814d015 100644 (file)
--- 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 $\log_aa = 1$
 
 $\log_a(m^{-1}) = -\log_am$  
 $\log_a1 = 0$ and $\log_aa = 1$
 

+

 ## Inverse functions
 
 Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$
 ## 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, $k < 0$
 $k$ 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
+
+