Give the equation of the horizontal asymptote, if any, of the function.
-$$h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$$
A) $y = 4$
B) no horizontal asymptote
C) $\mathrm { y } = 0$
D) $y = \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The degree of the numerator (3) is greater than the degree of the denominator (1), which means the function does not have a horizontal asymptote. Horizontal asymptotes are determined by comparing the degrees of the polynomial in the numerator and denominator. When the degree of the numerator is greater, the function grows without bound as $x$ approaches infinity, and thus, does not approach a constant value.

Give the Equation of the Horizontal Asymptote, If Any, of the Function