How do you write write #f(x)=|x-4|# as a piecewise function? Precalculus Functions Defined and Notation Function Composition 1 Answer A. S. Adikesavan Apr 10, 2016 #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#.. Answer link Related questions What is function composition? What are some examples of function composition? What are some common mistakes students make with function composition? Is function composition associative? Is it always true that #(f@g)(x) = (g@f)(x)#? If #f(x) = x + 3# and #g(x) = 2x - 7#, what is #(f@g)(x)#? If #f(x) = x^2# and #g(x) = x + 2#, what is #(f@g)(x)#? If #f(x) = x^2# and #g(x) = x + 2#, what is #(g@f)(x)#? What is the domain of #(f@g)(x)#? What is the domain of the composite function #(g@f)(x)#? See all questions in Function Composition Impact of this question 3431 views around the world You can reuse this answer Creative Commons License