A horizontal asymptote of a function f(x) is given by y = lim f(x) as x --> ∞ and x --> –∞. In this case,
[tex] \lim_{x \to \infty} \frac{-2x}{x+1} = \lim_{x \to \infty} \frac{-2x}{x(1+ \frac{1}{x} )}\\
=\lim_{x \to \infty} \frac{-2}{1+ \frac{1}{x} }\\
= -2
[/tex]
Thus, the horizontal asymptote of f(x) is y = –2.
