Question

Determine the horizontal asymptote of the given function. If none exists, state that fact. h(x)=6x²+9 / 8x³−3x−2

A) y=8
B) y=34
C) y=0
D) no horizontal asymptotes

Answer 1

D, and the horizontal hazmat is always the powers of the numerator and denominator

Answer 2

The horizontal asymptote of the function h(x) = (6x² + 9) / (8x³ - 3x - 2) is found by comparing the degrees of the numerator and the denominator. Since the numerator has a lower degree than the denominator, the horizontal asymptote is y = 0.

Step-by-step explanation:

To determine the horizontal asymptote of the function h(x) = (6x² + 9) / (8x³ - 3x - 2), you need to look at the degrees of the polynomial in the numerator and the denominator. In this case, the degree of the numerator is 2 (due to the term 6x²), and the degree of the denominator is 3 (due to the term 8x³). Since the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is at y = 0. Hence, the correct answer is C) y=0.