Domain and Range of Rational Functions

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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