Find the horizontal asymptote, if any.of the graph of the rational function. f(x)=(15x)/(5x^2)+9 Select the correct choice below and, if necessary, fill in the answer box to complete your A. The horizontal asymptote is square (Type an equation.) B. There is no horizontal asymptote.

To determine the horizontal asymptote of the rational function \( f(x) = \frac{15x}{5x^2 + 9} \), we need to compare the degrees of the polynomial in the numerator and the polynomial in the denominator.<br /><br />1. **Degree of the numerator**: The degree of the polynomial in the numerator, \( 15x \), is 1.<br />2. **Degree of the denominator**: The degree of the polynomial in the denominator, \( 5x^2 + 9 \), is 2.<br /><br />The rules for finding horizontal asymptotes are as follows:<br /><br />- If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is \( y = 0 \).<br />- If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is \( y = \frac{\text{leading coefficient of the numerator}}{\text{leading coefficient of the denominator}} \).<br />- If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.<br /><br />In this case, the degree of the numerator (1) is less than the degree of the denominator (2). Therefore, the horizontal asymptote is:<br /><br />\[ y = 0 \]<br /><br />So, the correct choice is:<br /><br />A. The horizontal asymptote is \( y = 0 \).