Definition of Asymptotes I dont understand

the function is ( x - 1 ) / x^2

in the back of the book it says there is a horizontal asymptote at y = 0
however x crosses that horizontal asymptote at x = 1


to find the horizontal asymptote, you find the limit as x approaches (+)(-) infinty
in this case the bottom exponent is bigger so there is always a horizontal asymptote at y = 0....... ?

I thought the whole point of asymptotes were to act as restrictions that a function(s) can never cross.

someone explain this to me please?

You are absolutely correct about the equations for the asymptotes..just remember a nice rule...

functions can sometimes cross the horizontal asymptotes but can NEVER cross the vertical asymptotes

The function can cross an asymptote at any point - what an asymptote REALLY indicates is the end behavior of a function - in other words, what the function eventually does as it gets closer and closer to infinity (in x or y). Basically, it says that eventually, the function will get closer and closer to some number without actually reaching that number, but along the way it may cross the asymptote. Don't think of it as a barrier, but rather a line that indicates the value that the function finally settles down along but does not come into contact with as it approaches infinity.