Let g(x)= cases x^ 2 -9 x-3 , & x 3, 6, & x=3

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

Problem

Let

g(x)=\begin{cases}\dfrac{x^{2}-9}{x-3}, & x\neq 3,\\ 6, & x=3.\end{cases}

Determine whether

g

is continuous at

x=3

and state your conclusion as “continuous” or “not continuous.”