The "basic" exponential function is the function
where is some positive constant.
For example, the graph of looks like this:
) The -intercept is (no matter what the value of is).
) The graph approaches the -axis asymptotically as goes to negative infinity (or as goes to positive infinity, if ).
) The graph is always positive (never zero or negative).
The exponential function can be shifted units upwards and units to the right with the equation:
Graph the equation.
Start with the "basic" exponential graph . Then shift the graph three units to the right and two units up.