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.

exponential graphs

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  
\[(\frac{1}{k} ln(\frac{B}{A}),0)\]
.