horizontal asymptotes of \( F(x)=\frac{3 x}{x^{2}-4} \) \( \begin{array}{ll}\text { Jone } & \text { B. } y=-2,2\end{array} \)

To determine the horizontal asymptotes of \( F(x)=\frac{3 x}{x^{2}-4} \), we look at the degrees of the polynomial in the numerator (degree 1) and denominator (degree 2). When the degree of the numerator is less than that of the denominator, the horizontal asymptote is determined by \( y=0 \). Therefore, the correct horizontal asymptote for this function is \( y=0 \). As a common mistake, students often misinterpret the coefficients or constant terms when identifying horizontal asymptotes. Remember, it’s all about the degrees of polynomials! If the numerator's degree equals the denominator's, the asymptote is \( y=\frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}} \).