Domain and Range for Absolute Value Functions

Find the domain and range for each of the absolute value functions that follow. Adjust the sliders to transform the general absolute value function f(x) = a |x - h| + k.  

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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 an absolute value 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) = |x|. Which of the values a, h, or k have a role in determining the range? Why? Use specific examples to support your claims.

Duke, 11/11/06, Created with GeoGebra

  1.  f(x) = 2 |x-4| + 1

  2.  f(x) = -3 |x+1| + 4

  3.  f(x) = |x-2|

  4.  f(x) = .4 |x+3| - 3

  5.  f(x) = 7 - 3 |x-4|