Question

Range of the function $f\left(x\right)=|x-1|+|x-2|+|x+1|+|x+2|$ where $xϵ[-2,2]$, is

• A. [6,8]
• B. [2,4]
• C. [0,4]
• D. {1,2}

Answer 1

The correct option is A

[6,8]

$f\left(x\right)=|x-1|+|x-2|+|x+1|+|x+2|$
When $xϵ[-2,-1]f\left(x\right)=-(x-1)-(x-2)-(x+1)+x+2=-2x+4$
When $xϵ[-1,1],f\left(x\right)=-(x-1)-(x-2)+x+1+x+2=6$
When $xϵ[1,2],f\left(x\right)=(x-1)-(x-2)+x+1+x+2=2x+4$
Plotting the graph of the function, range of $f\left(x\right)=[6,8]$