From: Andrew Lorimer 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 + +