009A Sample Final 2, Problem 2

Let

$f(x)=\left\{{\begin{array}{lr}{\frac {x^{2}-2x-3}{x-3}}&{\text{if }}x\neq 3\\5&{\text{if }}x=3\end{array}}\right.$

For what values of  $x$  is  $f$  continuous?

Foundations:
$f(x)$  is continuous at  $x=a$  if
$\lim _{x\rightarrow a^{+}}f(x)=\lim _{x\rightarrow a^{-}}f(x)=f(a).$

Solution:

Step 1:

Step 2:

Final Answer:

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