## Domain and Range of Radical Functions

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

Find the

domain and

range for each of the square root functions that follow. Adjust the sliders to transform the general square root function

f(x) = a (x - h)^{1/2} + k
Duke, 11/11/06, Created with GeoGebra

## Investigation Steps

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

Journal Entry:

Describe how the values of a, h, and k can be used to find the domain and range of a square root function in the form

f(x) = a (x - h)^{1/2} + k. Compare the domain and range of

f(x) = a (x - h)^{1/2} + k to the domain and range of its parent function f(x) = x^{1/2}. Which of the values a, h, or k have a role in determining the domain and range? Why? Usespecific examples to support your claims.

- f(x) = 2 (x - 4)
^{1/2}

- f(x) = 2 (x - 1)
^{1/2} + 2

- f(x) = -1 (x + 2)
^{1/2} + 3

- f(x) = .2 (x - 2)
^{1/2} - 2