Let . Which of the following best explains the long-run behavior of…

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

Problem

Let

h(x)=\dfrac{5x^{3}+1}{e^{x}}

. Which of the following best explains the long-run behavior of

h

? (a)

h

has no horizontal asymptote because the numerator is a higher-degree polynomial than the denominator. (b)

h

has a horizontal asymptote at

y=5

because the leading coefficient of the numerator determines the end behavior. (c)

h

has a horizontal asymptote at

y=0

because the exponential in the denominator eventually grows faster than any polynomial numerator. (d)

h

has a horizontal asymptote at

y=0

because as

x\to-\infty

the denominator

e^{x}

approaches

0