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Exponential Functions

The "basic" exponential function is the function

where a is some positive constant.

For example, the graph of y = 2^x looks like this:

Note that:

1) The y-intercept is 1 (no matter what the value of a is).

2) The graph approaches the x-axis asymptotically as x goes to negative infinity (or as x goes to positive infinity, if 0 a 1).

3) The graph is always positive (never zero or negative).

The exponential function can be shifted k units upwards and h units to the right with the equation:

Start with the "basic" exponential graph y = 2^x. Then shift the graph three units to the right and two units up.