The graph of the exponential function $y=b\cdot g^x$ has the following characteristics:

• The graph intersects the $y$ -axis in the point $\left(\mathrm{0,}b\right)$

• When $b>0$ and $g>1$, the graph is increasing. To the left (for decreasing $x$) the graph approaches the $x$ -axis. The function value can be made to be as close to $0$ as you want by chosing $x$ sufficiently small. The $x$ -axis is the horizontal asymptote.

• When $b>0$ and $0<g<1$, the graph is decreasing. To the right (for increasing $x$) the graph approaches the $x$ -axis, the horizontal asymptote.

• When $b<0$ and $0<g<1$, the graph is increasing. To the right (for increasing $x$) the graph approaches the $x$ -axis, the horizontal asymptote.

• When $b<0$ and $g>1$, the graph is decreasing. To the left (for decreasing $x$) the graph approaches the $x$ -axis, the horizontal asymptote.

• When $g=1$ the graph is a horizontal line $y=b$.

Exponential equations like $b\cdot g^x=a$ can be solved using the GRC. For exponential inequalities you use the properties above.