Question

Identify the horizontal asymptote of f(x) = 2x³ / (x² - 5).

1) y = 0
2) y = 1/2
3) y = 2
4) There is no horizontal asymptote

Answer 1

The function f(x) = 2x³ / (x² - 5) does (4) not have a horizontal asymptote since the degree of the numerator is greater than the degree of the denominator.

Step-by-step explanation:

To identify the horizontal asymptote of the function f(x) = 2x³ / (x² - 5), we compare the degrees of the polynomial in the numerator and the denominator. Since the degree of the numerator (3) is greater than the degree of the denominator (2), this function does not have a horizontal asymptote.

Horizontal asymptotes typically occur when the degree of the numerator is less than or equal to the degree of the denominator. Therefore, none of the given options (y = 0, y = 1/2, y = 2) is a correct answer, making option 4 (There is no horizontal asymptote) the correct choice for this function.