## Domain and Range of Rational Functions

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

Find the domain and range for each of the rational functions that follow. Adjust the sliders to transform the general rational function f(x) = a / (x - h) + k.   In addition, list all vertical and horizontal asymptotes.

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Duke, 11/11/06, Created with GeoGebra

## Investigation Steps

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

1. f(x) = 1 / x + 2

2. f(x) = 1 / (x - 4) - 1

3. f(x) = -2 / (x + 1) + 3

4. f(x) = 10 / (x - 3) + 4