## Domain and Range for Exponential Functions

**READ** the instructions on the *right* and **INTERACT** with the GeoGebra applet below.

Move the sliders to transform the parent exponential function *f(x) = b*^{x} into the function

*f(x) = a*b*^{x-h} + k. Write the domain, range and the equation of the horizontal asymptote for each of the examples that follow. In addition, classify each equation as growth or decay when appropriate.

Duke, 11/11/06, Created with GeoGebra

## Investigation Steps

To RESET the construction, click on the browser's Refresh button.

Journal Entry:

Describe each variable's effect on the domain, range, and end behavior of the exponential function

*f(x) = a*b*^{x-h} + k. Make a table if necessary.

- f(x) = 3
^{x} + 3
- f(x) = 4*(.5)
^{x-3} - 1
- f(x) = -3*5
^{x-1} + 4
- f(x) = 9*10
^{x-5}