Question

Which of the following options is/are true for the function $f\left(x\right)=|x-3|+|x-4|$

• A. The minimum value of $f\left(x\right)$ is $1$
• B. $f\left(x\right)=2x-7$ when $x\ge 4$
• C. $f\left(x\right)=1$ when $x<3$
• D. The graph of $f\left(x\right)$ is
  

Answer 1

Answer: (A), (B), (D)

The correct options are
A The minimum value of $f\left(x\right)$ is $1$
B $f\left(x\right)=2x-7$ when $x\ge 4$
D The graph of $f\left(x\right)$ is


$f\left(x\right)=|x-3|+|x-4|$
$f\left(x\right)=\{\begin{array}{cc}-2x+7,& x<3\\ 1,& 3\le x<4\\ 2x-7,& x\ge 4\end{array}$

Graph of $f\left(x\right)$ is


From graph, the minimum value of $f\left(x\right)$ is $1$