Question

The minimum value of the expression is $y=|x+1|+|x-3|$ is

• A. $0$
• B. $1$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

$y=|x+1|+|x-3|$
Here the turning points are $-1,3$
$y=\{\begin{array}{cc}-(x+1)-(x-3),& x<-1\\ (x+1)-(x-3),& -1\le x<3\\ (x+1)+(x-3),& x\ge 3\end{array}\Rightarrow y=\{\begin{array}{cc}2-2x,& x<-1\\ 4,& -1\le x<3\\ 2x-2,& x\ge 3\end{array}$


Hence, the minimum value of the expression is $4$.