Question

Identify the horizontal asymptote of the rational function?

1) The function doesn't have a horizontal asymptote.
2) y = 3
3) y = 4
4) y = 0

Answer 1

The horizontal asymptote of a rational function can be determined by examining the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, the horizontal asymptote is a horizontal line defined by the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Step-by-step explanation:

The horizontal asymptote of a rational function can be identified by examining the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, the horizontal asymptote is a horizontal line defined by the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

From the given options, the correct answer is: 1) The function doesn't have a horizontal asymptote.