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Given the piecewise function:

$$f( x ) =\begin{cases} { 2x }^{ 2 }+1,\quad x<-1 \\\ 2x+5,\quad x\ge -1 \end {cases}$$

...which of the following statements are true?

I. $f$ is continuous at $x=-1$
II. $f$ is differentiable at $x=-1$
III. $\lim_{x\xrightarrow{}{-1}^{-}}{f(x)=\lim_{x\xrightarrow{}{-1}^{+}}{f(x)}}$

A

I only.

B

I and II only.

C

I and III only.

D

I, II, and III.

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