Question

How do you write write `f(x)=|x-4|` as a piecewise function?

Answer 1

`f(x)=x-4, x>=4 and f(x)=-(x-4), x<=4`, representing radial lines from [4, 0], with slopes `+-1`. It is implicit that `f(x)>=0`... .

Explanation:

`f(x)=|x-4|` is the combined equation for the half-line equations `f(x) = x-4, x>=4 and f(x)=4-x, x<=4`.
Note that `f(x)>=0`..