The function is defined by h(x)= cases x^ 2 -4 x-2 , & x3

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

Problem

The function

h

is defined by

h(x)=\begin{cases} \dfrac{x^{2}-4}{x-2}, & x<2,\\ a, & x=2,\\ \dfrac{x^{2}-9}{x-3}, & 2<x<3,\\ b, & x=3,\\ x+1, & x>3. \end{cases}

To eliminate only the removable discontinuities of

h

while leaving any non-removable discontinuities unchanged, which set of ordered pairs must be included in the graph? (a)

(2,4) \text{ and } (3,6)

(b)

(2,4) \text{ only}

(c)

(2,4) \text{ and } (3,4)

(d)

(3,6) \text{ only}