Suppose $f(x)$ is defined as shown below.

a$.$ Use the continuity checklist to show that f is not continuous at $2.$

b$.$ Is f continuous from the left or right at $2?$

c$.$ State the interval$($s$)$ of continuity.

$f(x)=\{\begin{array}{ccc}{x}^2+2x& if& x2\\ 3x& if& x<mn>2</mn>\end{array}$

a$.$ Why is f not continuous at $2?$

A$.\underset{x2}{lim}f(x)$ does not exist

B$.$ Although $\underset{x2}{lim}f(x)$ exists, it does not equal $f(2).$

C$.f(2)$ is not defined.

b$.$ Choose the correct answer below.

A$.f$ is continuous from the right at $2.$

B$.f$ is continuous from the left at $2.$

C$.f$ is not continuous from the left or the right at $2.$

c$.$ What are the interval$($s$)$ of continuity?