Graphs of Exponential Functions

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A general exponential function has the form , where and are positive real numbers. The number is called the exponential base and the number is called the multiplicative constant.


If the base , then the function is one of exponential growth and the function is always increasing. If the base , then the function is one of exponential decay and is therefore always decreasing.


Contributed by: Laura R. Lynch (June 2014)
Open content licensed under CC BY-NC-SA



There are two special points to keep in mind to help sketch the graph of an exponential function: At , the value is and at , the value is .

Here are three other properties of an exponential function:

• The intercept is always at .

• There are no intercepts. In fact, the exponential function has horizontal asymptote at

• The graph is always above the axis.

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