Question

can horizontal asymptotes crosswith the lines of the function?

Answer 1

"In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity."

http://en.wikipedia.org/wiki/Asymptote

So, not usually (unless your book is one of them other authors)

Answer 2

ok sare any of these equations ok with a horizonta; asy of y=2
1. Y=2(x+1)^2/x^2-4
2. 2(x+5)^2/x^2-1
can one and two be ok with having a HA at y=2

Answer 3

You just need a graph to check your rule for asymptotes

Your first one is here (think I got your equation right)

http://www.wolframalpha.com/input/?i=Y%3D2%28x%2B1%29^2%2F%28x^2-4%29

Answer 4

the 2 isn't in from of the equation, it's on top of that equation.