Question

The difference between the maximum and minimum value of the expression $y=|x-9|-|x+2|$ is

• A. $-11$
• B. $0$
• C. $11$
• D. $22$

Answer 1

The correct option is D $22$

$y=|x-9|-|x+2|$
Here the turning points are $-2,9$

$y=\{\begin{array}{cc}-(x-9)+(x+2),& x<-2\\ -(x-9)-(x+2),& -2\le x<9\\ (x-9)-(x+2),& x\ge 11\end{array}\Rightarrow y=\{\begin{array}{cc}11,& x<-2\\ 7-2x,& -2\le x<9\\ -11,& x\ge 9\end{array}$


Here, the maximum value of $y=11$
Minimum value of $y=-11$

Hence, the difference $=11-(-11)=22$