Take a look at the applet: Exponential Function
The graph of the exponential function has the following characteristics:
The graph intersects the -axis at the point .
If and the graph is increasing. To the left (for decreasing ) the graph approaches the -axis. You can take the function value as close to as you like by taking sufficiently small. The -axis is the horizontal asymptote.
If and the graph is decreasing. To the right (for increasing ) the graph approaches the -axis, the horizontal asymptote.
If and the graph is increasing. To the right (for increasing ) the graph approaches the -axis, the horizontal asymptote.
If and the graph is decreasing. To the left (for decreasing ) the graph approaches the -axis, the horizontal asymptote.
If the graph is the horizontal line .
Exponential equations like can be solved using the calculator.
For exponential inequalities one uses the properties mentioned above .