Given $f ( x ) = \left\{ \begin{array} { l } - 2 x \text { if } x < 1 \\x - 3 \text { if } x \geq 1\end{array} \right.$

Multiple Choice

Given $f ( x ) = \left\{ \begin{array} { l } - 2 x \text { if } x < 1 \\x - 3 \text { if } x \geq 1\end{array} \right.$ , is $f$ continuous and/or differentiable at $x = 1 ?$ Explain.

A) f is not continuous but differentiable at x = 1
B) f is neither continuous nor differentiable at x = 1
C) f is continuous but not differentiable at x = 1
D) f is both continuous and differentiable at x = 1