Decreasing from the horizontal asymptote The function $f(x) = x^2/(x^2 - x -2)$ has the following graph. It has a horizontal asymptote $y=1$. For $x$ less than $-4$, the function is decreasing and its graph is under the asymptote. How is this possible when $\lim_{n \to -\infty} f(x) = 1$? Can a function decrease away from its vertical asymptote?

The definition of increasing is $$ x_1
Maybe the following example will make things clear. $x^2$ decreases on $(-\infty,0)$, but $\lim_{x\to-\infty}x^2=+\infty$.