Which statement correctly describes the behavior of the graph of at ?

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

Problem

Which statement correctly describes the behavior of the graph of

g(x)=\dfrac{x^{2}-5x+4}{x-2}

x=2

? (a) The graph has a horizontal tangent at

x=2

because

g'(2)=0

. (b) The graph has a vertical tangent at

x=2

because

g'(2)

is undefined while

g(2)

exists. (c) The graph has no tangent at

x=2

because

g

is not defined there. (d) The graph has a tangent of slope

1

x=2

after canceling a common factor.