Question

The range of the function $f\left(x\right)=|x-1|+|x-2|,-1\le x\le 3$ is

• A. $[1,3]$
• B. $[1,5]$
• C. $[3,5]$
• D. $[1,5)$

Answer 1

The correct option is B $[1,5]$

$f\left(x\right)=|x-1|+|x-2|$
$1\le x\le 3$
$case1$
$whenx<1$
$f\left(x\right)=-(x-1)-(x-2)$
$=-2x+3$
$case2$
$when1\le x\le 2$
$f\left(x\right)=(x-1)-(x-2)$
$=x-1-x+2$
$=1$
$case3$
$whenx\ge 2$
$f\left(x\right)=(x-1)+(x-2)$
$=2x-3$
$Hencefromgraph$
$Range:[1,5]$