find the horizontal asymptote, if any, of the graph of the rational function.\n\n$f(x)=\\frac{12x}{3x^{2}+2}$…

find the horizontal asymptote, if any, of the graph of the rational function.\n\n$f(x)=\\frac{12x}{3x^{2}+2}$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the horizontal asymptote is \\square. (type an equation.)\nb. there is no horizontal asymptote.

find the horizontal asymptote, if any, of the graph of the rational function.\n\n$f(x)=\\frac{12x}{3x^{2}+2}$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the horizontal asymptote is \\square. (type an equation.)\nb. there is no horizontal asymptote.

Answer

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator (12x) (where the highest - power of (x) is (n = 1)) and the degree of the denominator (3x^{2}+2) (where the highest - power of (x) is (m=2)).

Step2: Apply the rule for horizontal asymptotes of rational functions

For a rational function (y=\frac{f(x)}{g(x)}=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}), if (n\lt m), then (y = 0) is the horizontal asymptote. Since (n = 1) (degree of numerator) and (m = 2) (degree of denominator) and (1\lt2).

Answer:

A. The horizontal asymptote is (y = 0)