Mathematics

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.