# For the function f(x)= l x-5 l find the domain and the range. Must show work and write answer using interval notation.

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You need to use absolute value definition for |x - 5| such that:

`|x - 5| = x - 5 if x - 5 gt 0 =gt x gt 5 =gt x in (5,oo)` `|x - 5| = 0 if x - 5 = 0 =gt x = 5` `|x- 5| = 5 - x if x - 5 lt 0 =gt x lt 5 =gt x in (-oo,5)`

Notice that the values of x cover all real set, hence domain of function f(x)=|x-5| is R set.

You should notice that the values of the function are always positive for any value of x, hence the range of function is the interval [0,oo).

Sketching the graph of the function below, you may notice that the graph is symmetric to y axis.

**Hence, the domain of the function is R set and the range is `[0,oo)` .**

This question has been answered at: http://www.enotes.com/math/q-and-a/function-f-x-l-x-5-l-find-domain-range-write-your-331988