Question

Find the horizontal asymptote of the graph of y = -4x^6 + 6x + 3/8x^6 + 9x + 3
y=1
y=-1/2
y=0
There is no horizontal asymptote.

Answer 1

Option B : $y=-\frac{1}{2}$ is the horizontal asymptote.

Explanation:

The function is $y=\frac{-4 x^{6}+6 x+3}{8 x^{6}+9 x+3}$

The horizontal asymptote can be determined by

$y=\frac{leading \ coefficient \ of \ numerator}{leading \ coefficient \ of \ denominator}$

Thus, from the function, the leading coefficient of numerator is -4

The leading coefficient of denominator is 8

Thus, substituting the values in the formula $y=\frac{leading \ coefficient \ of \ numerator}{leading \ coefficient \ of \ denominator}$ , we get,

$y=\frac{-4}{8}$

Dividing, we get,

$y=\frac{-1}{2}$

Thus, the horizontal asymptote is $y=\frac{-1}{2}$

Hence, Option B is the correct answer.