Consider the rational function

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

P(V)=\dfrac{2V^{2}-k}{V^{2}-9}

, which models the pressure (in kPa) of a gas as a function of its volume

V

(in L) for

V\neq3

. For which value of

k

will the graph of

P

have a removable discontinuity (a hole) rather than a vertical asymptote at

V=3

? (a)

k=6

(b)

k=9

(c)

k=18

(d)

k=27