## Exponential Graphs

The general equation of an exponential graph is
$y=A+B^{kx}$
.
Each pf
$A, \: B, \: k$
can be positive or negative and the sign and magnitude of each determines the shape of the graph.
The graph has an asymptote in the line
$y=A$
. If
$B \gt 0$
, the graph lies above the asymptote. If
$B \lt 0$
the graph is below the asymptote.

The intercept with the
$y$
- axis is at
$(0,A+B)$
.
There is no
$x$
- intercept if
$A=0$
or if
$A, \: B$
have the same sign. If
$A, \: B$
have opposite signs then the
$x$
intercept is at
$(\frac{1}{k} ln(\frac{B}{A}),0)$
.