Let . Which statement about the discontinuities of is…

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

Problem

Let

h(x)=\dfrac{x^{3}-3x^{2}-4x+12}{x^{2}-4}

. Which statement about the discontinuities of

h

is true? (a)

h

has vertical asymptotes at

x = 2

and

x = -2

and no removable discontinuities. (b)

h

has a removable discontinuity at

x = 2

and a vertical asymptote at

x = -2

. (c) The graph has removable discontinuities at

x = 2

and

x = -2

and no vertical asymptotes. (d) The function is continuous for all real

x

because the factor

x^{2}-4

cancels completely.