Find the horizontal​ asymptote, if​ any, of the graph of the rational function.

Question

f(x)=16x/6x62+1

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. The horizontal asymptote is blank. ​(Type an​ equation.)
B. There is no horizontal asymptote.

Answer 1

To find the horizontal asymptote of the rational function \( f(x) = \frac{16x}{6x^2 + 1} \), we analyze the degrees of the polynomial in the numerator and the polynomial in the denominator.

1. The degree of the numerator (which is \( 16x \)) is 1.
2. The degree of the denominator (which is \( 6x^2 + 1 \)) is 2.

Since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote of the function is given by:

\[ y = 0 \]

Thus, the horizontal asymptote is:

A. The horizontal asymptote is \( y = 0 \).