Find the horizontal and verlical asymptotes of \( f(x) \). \( f(x)=\frac{7 x}{x+4} \) Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice A. The function has one horizontal asymptote, (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is (Type equations.) C. The function has no horizontal asymptotes.

To find the horizontal asymptotes of \( f(x) = \frac{7x}{x + 4} \), we look at how the function behaves as \( x \) approaches infinity or negative infinity. Since the degrees of the numerator and denominator are the same (both are degree 1), the horizontal asymptote can be found by taking the ratio of the leading coefficients. Here, the leading coefficient of the numerator is 7 and the leading coefficient of the denominator is 1. Thus, the horizontal asymptote is \( y = \frac{7}{1} = 7 \). The choice would be: A. The function has one horizontal asymptote, \( y = 7 \). For the vertical asymptote, we find where the function is undefined, which occurs when the denominator equals zero. Setting \( x + 4 = 0 \) gives \( x = -4 \). Therefore, the vertical asymptote is at \( x = -4 \). So, the vertical asymptote is: The vertical asymptote is \( x = -4 \).