Consider the following function.

$f(x)=\{\begin{array}{ccc}x-6& if& x2\\ 2x-0& if& x>2\end{array}$

Find each value. $($If an answer does not exist, enter DNE.$)$

$f(2)=$

$\underset{x{2}^{-}}{lim}f(x)=$

$\underset{x{2}^{+}}{lim}f(x)=$

Determine whether the function is continuous or discontinuous at $x=2.$ Examine the three conditions in the definition of continuity.

The function is continuous at $x=2.$

The function is discontinuous at $x=2.$