Question

What is the horizontal asymptote of a rational function where the denominator is a radical function?

a) There is no horizontal asymptote
b) The horizontal asymptote is the x-axis (y=0)
c) The horizontal asymptote is the y-axis (x=0)
d) The horizontal asymptote depends on the specific radical function in the denominator

Answer 1

The horizontal asymptote of a rational function with a radical denominator depends on the specific radical function in the denominator.

Step-by-step explanation:

The horizontal asymptote of a rational function where the denominator is a radical function depends on the specific radical function in the denominator. Option d) The horizontal asymptote depends on the specific radical function in the denominator is the correct answer.

For example, consider the rational function y = 1/sqrt(x). As x approaches infinity or negative infinity, the denominator sqrt(x) approaches infinity. Therefore, the function approaches zero and the horizontal asymptote is the x-axis (y = 0).