How do you write #p(x) = |x-1| +4# as a piecewise function?

1 Answer
Sep 7, 2017

Answer:

#p(x)=-x+5 :x in (-oo,1)#
#p(x) = +x+3: x in [1, +oo)#

Explanation:

#p(x) =abs(x-1)+4#

#p(x) =-(x-1)+4 =-x+5#
where #x-1<0 -> x in (-oo, +1)#

#p(x) =+(x-1)+4 = +x+3#
where #x-1>=0 -> x in [1, +oo)#

This can be more easily visualised from the graph pf #p(x)# below.

graph{abs(x-1)+4 [-9.96, 10.04, -0.64, 9.36]}