Determine whether the following function is continuous at a$.$ Use the continuity checklist to justify your answer.

f$($x$)=$

$*-9$

x$-3$

if x#$3$

; a $=3$

if x $=3$

$$ Question $2.$

Question $3$

$$ Question $4$

Select all that apply.

$$A$.$ The function is continuous at a $=3.$

$$B$.$ The function is not continuous at a $=3$ because f$(3)$ is undefined.

$$The function is not continuous at a $=3$ because lim $($x$)$ does not exist.

$$The function is not continuous at a $=3$ because lim $($x$)$ # $1(3).$