Question

If $f\left(x\right)=\left|x\right|+|x-1|$, then which one of the following is correct?

• A. $f\left(x\right)$ is continuous at $x=0$ and $x=1$
• B. $f\left(x\right)$ is continuous at $x=0$ but not at $x=1$
• C. $f\left(x\right)$ is continuous at $x=1$ but not at $x=0$
• D. $f\left(x\right)$ is neither continuous at $x=0$ nor at $x=1$

Answer 1

The correct option is A $f\left(x\right)$ is continuous at $x=0$ and $x=1$

The graph of $f\left(x\right)=|x|+|x-1|$ is shown below

Clearly $f\left(x\right)$ is continuous at $x=0$ and $x=1$