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) $y = 0$
D) $y = \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

For the function $h(x) = \frac{4x^3 - 5x - 9}{8x + 3}$, the degree of the numerator (3) is greater than the degree of the denominator (1), which means there is no horizontal asymptote. Horizontal asymptotes occur when the degrees of the numerator and denominator are equal or the degree of the denominator is greater.

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