# How do you find the asymptotes for y = (x^2-2x)/(x^2-5x+4)?

Dec 20, 2015

The asymptote is $y = 1$.
In order to know if $f \left(x\right) = \frac{{x}^{2} - 2 x}{{x}^{2} - 5 x + 4}$, you need the limit of $f$ when $x$ becomes infinite.
We know that in a rational function, only the highest power matters at the infinites. So we can say that ${\lim}_{+ \infty} f = 1$ and it means that the line $y = 1$ is an asymptote when $x$ becomes really big, and it is the exact same thing when $x \to - \infty$. It's quite visible on the graph.