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

1 Answer
Topscooter
Dec 20, 2015

The asymptote is y = 1.

Explanation:

In order to know if f(x) = (x^2 - 2x)/(x^2-5x+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_(+oo) 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 -> -oo. It's quite visible on the graph.

graph{(x^2 -2x)/(x^2 - 5x + 4) [-8.66, 11.34, -3.24, 6.76]}

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