Consider the function q(x)= cases x^2-9 x-3 , & x<3, (x-3)^3, & x 3

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

Problem

Consider the function

q(x)= \begin{cases} \dfrac{x^2-9}{x-3}, & x<3,\\ (x-3)^3, & x\ge 3. \end{cases}

Does

q

have a vertical asymptote at

x=3

? Justify your answer using limits.