Consider the following.

$f(x)=\{\begin{array}{cc}6-2x,& x3\\ x^2-2,& x>3\end{array}$

Describe the interval$($s$)$ on which the function is continuous. $($Enter your answer using interval notation.$)$

Identify any discontinuities. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=$

$$

If the function has any discontinuities, identify the conditions of continuity that are not satisfied. $($Select all that apply. Select each choice if it is met for any of the discontinuities.$)$

There is a discontinuity at $x=c$ where $f(c)$ is not defined.

There is a discontinuity at $x=c$ where $\underset{xc}{lim}f(x)f(c).$

There is a discontinuity at $x=c$ where $\underset{xc}{lim}f(x)$ does not exist.

There are no discontinuities; $f(x)$ is continuous.