## Exponential Graphs

\[y=A+B^{kx}\]

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

.