The range of the function f(x)=|x−1|+|x−2| , −1≤x≤3, is

Clearly, from the graph, the range is [1,f(−1)]≡[1,5] .  If x<1,f(x)=−(x−1)−(x−2)=−2x+3 In this interval, f(x) is decreasing.  If 1≤x<2,f(x)=x−1−(x−2)=1 In this interval, f(x) is constant.  If 2≤x≤3,f(x)=x−1+x−2=2x−3 .  In this interval, f(x) is increasing. ∴maxf(x)= the greatest among f(−1) and f(3)=5minf(x)=f(1)=1 So, range =[1,5]