MCQ

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Consider the function :$f\left( x \right) = \left[ x \right] + \left| {1 - x} \right|,\, - 1 \le x \le 3$ where $[x]$ is the greatest integer function
Statement $1 :f$ is not continuous at $x = 0, 1, 2$ and $3$
Statement $2 :f\left( x \right) = \left( \begin{array}{l}  - x,\,\,\,\,\,\,\,\,\, - 1 \le x < 0\\ 1 - x,\,\,\,\,\,\,\,0 \le x < 1\\ 1 + x,\,\,\,\,\,\,\,1 \le x < 2\,\\ 2 + x,\,\,\,\,\,\,2 \le x \le 3 \end{array} \right.$

• A
  Statement $1$ is true ; Statement $2$ is false,
• B
  Statement $1$ is true; Statement $2$ is true;Statement $2$ is not correct explanation for Statement $1$
• C
  Statement $1$ is true; Statement $2$ is true;Statement It is a correct explanation for Statement $1$.
• D
  Statement $1$ is false; Statement $2$ is true