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

Multiple Choice

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

A) f is continuous but not differentiable at x = 2
B) f is differentiable but not continuous at x = 2
C) f is neither continuous nor differentiable at x = 2
D) f is both continuous and differentiable at x = 2