The graph of the exponential function has the following characteristics:
The graph intersects the -axis in the point
When and , the graph is increasing. To the left (for decreasing ) the graph approaches the -axis. The function value can be made to be as close to as you want by chosing sufficiently small. The -axis is the horizontal asymptote.
When and , the graph is decreasing. To the right (for increasing ) the graph approaches the -axis, the horizontal asymptote.
When and , the graph is increasing. To the right (for increasing ) the graph approaches the -axis, the horizontal asymptote.
When and , the graph is decreasing. To the left (for decreasing ) the graph approaches the -axis, the horizontal asymptote.
When the graph is a horizontal line .
Exponential equations like can be solved using the GRC. For exponential inequalities you use the properties above.