Question

what is the horizontal asymptote of $f(x)=\frac{-2x}{x + 1}$?

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator \( -2x \) (degree \( n = 1 \)) and the degree of the denominator \( x + 1 \) (degree \( m=1 \)).

Step2: Use the horizontal asymptote rule for \( n = m \)

When \( n=m \), the horizontal asymptote \( y=\frac{a_n}{b_m} \), where \( a_n\) is the leading coefficient of the numerator and \( b_m\) is the leading coefficient of the denominator. Here \( a_n=-2\), \( b_m = 1\). So \( y=\frac{-2}{1}=-2 \).

Answer:

\( y=-2 \)