Question

What is the horizontal asymptote of the graph of f(x) = 4x² / (2x - 12x³)? Give your answer in the form y = a.

a) y = 0
b) y = 1/6
c) y = -1/6
d) y = -[infinity]

Answer 1

The horizontal asymptote of the function f(x) = 4x² / (2x - 12x³) is y = 0, because the degree of the denominator is higher than that of the numerator.

Step-by-step explanation:

To determine the horizontal asymptote of the function f(x) = 4x² / (2x - 12x³), we need to look at the behavior of the function as x approaches infinity. The degree of the numerator is 2 (because of x²) and the degree of the denominator is 3 (because of x³). In a case where the degree of the denominator is higher than the numerator, the horizontal asymptote will be y = 0, because the fraction's value approaches zero as x grows large. Therefore, the answer is a) y = 0.