## 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.

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.

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

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

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

- f(x) =
^{10} / _{(x - 3)} + 4