Graphs of Exponential Functions
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.[more]
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.[less]
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.