Multiple Choice: Which of the following statements must be true of the function $f(x)$ defined below?
$f ( x ) = \left\{ \begin{array} { l l } { e ^ { x + 2 } - 1 } & { \text { for } \quad x \leq - 2 } \\ { 4 - x ^ { 2 } } & { \text { for } - 2 < x < 0.5 } \\ { 4 - \operatorname { cos } ( x - 0.5 ) } & { \text { for } \quad x \geq 0.5 } \end{array} \right.$

1. $f(x)$ is continuous at $x = −2$.

2. $f(x)$ is differentiable at $x = −2$.

3. $f(x)$ is differentiable at $x = 0.5$ .