2A-1. Exponential Functions
Instructions:
- Use the input boxes on the left to set the parameters and for the exponential function of the form . Use the slider tools to adjust these values and see how they effect the graph/behavior of the function.
- Use the input box for to set the location of the point . Use the slider tool for to set the location for the point .
- The text displays information to show how the -values of and are related through the growth/decay factor.
Exponential Functions
An exponential function has the form , where and are constants and is the independent variable. Notice that the coefficient determines the vertical intercept of the graph and that the growth factor determines the "steepness" of the graph.
The fundamental characteristic of an exponential function is that changes in the input correspond to repeated multiplication in the output. If you move 2 units in the direction (i.e., ), then you have to multiply the -coordinate by the growth/decay factor 2 times.
Based on the values of and , you should be able to predict whether the graph will be increasing or decreasing. Based on the shape of the graph, what can you say about the concavity?