Consider the function defined by f(x)= cases x^ 2 -4 x-2 ,& x 2 3,& x=2 cases

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the function defined by

f(x)=\begin{cases}\dfrac{x^{2}-4}{x-2},& x\ne 2\\3,& x=2\end{cases}.

Determine whether

f

is continuous at

x=2

and state the type of discontinuity if it is not.