Find the horizontal asymptote, if any, of the graph of the rational function. \( f(x)=\frac{15 x}{5 x^{2}+1} \)

To find the horizontal asymptote of the rational function \( f(x)=\frac{15 x}{5 x^{2}+1} \), we will analyze the degrees of the numerator and denominator. The degree of the numerator (which is linear, or degree 1) is less than the degree of the denominator (which is quadratic, or degree 2). In such cases, the horizontal asymptote is given by \( y = 0 \), meaning that as \( x \) approaches positive or negative infinity, the function approaches the line \( y = 0 \). For added fun, think of it as a race: the numerator is a sprinter, while the denominator is a long-distance runner. When they finish the marathon (or approach infinity), the sprinter can't keep up, and they both settle to rest at the finish line \( y = 0 \)!