Define f(x)= cases |x-2| x-2 , & x 2 [6pt]0, & x=2 cases and g(x)= f(x) x-4

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define

f(x)=\begin{cases}\dfrac{|x-2|}{x-2}, & x\ne2\\[6pt]0, & x=2\end{cases}\quad\text{and}\quad g(x)=\frac{f(x)}{x-4}.

Which statement correctly classifies the discontinuities of

g

? (a) Removable at

x=2

; vertical asymptote at

x=4

(b) Jump at

x=2

; vertical asymptote at

x=4

x=2

; removable at

x=4

(d) Vertical asymptotes at both

x=2

and

x=4