Assume \(a>0,\ a\ne1\).
Exponential graphs
\(a>1\) (growth): as \(x\) increases, \(y\) increases.
\(0<a<1\) (decay): as \(x\) increases, \(y\) decreases.
Logarithmic graphs
\(a>1\): increasing through \((1,0)\).
\(0<a<1\): decreasing through \((1,0)\).
Key features
| Graph | Domain | Range | Asymptote | Key point |
|---|---|---|---|---|
| \(y=a^x\) | ||||
| \(y=\log_a x\) |
Inverse functions
\(y=a^x\quad\Longleftrightarrow\quad x=\log_a y\)
The graphs reflect in \(y=x\): \((p,q)\) maps to \((q,p)\). Label intercepts and asymptotes.
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