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

1 Answer
Dec 20, 2015

Answer:

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]}