What is the domain and range of the function f(x) = |x - 2|

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain and range of the function f(x) = |x - 2| has to be determined. The domain of a function is all values of x for which the value of f(x) is defined. The range of the function is all values of f(x) for values of x that lie in the domain.

The absolute value function f(x) = |x| is defined as f(x) = x for x>=0 and f(x) = -x for x <0.

If f(x) = |x - 2| the value of f(x) is defined for all values of x. The domain of the function is the set of real numbers R. The value of f(x) = |x - 2| is never negative,. For value of x < 2, the function f(x) = 2 - x which is positive. The range of the function is therefore the set `[0, oo)` .

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