You are right to have those two asymptotes.
look at
http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x%5E2%2B4x-5%29%2F%28x-2%29+%2C+y+%3D+x%2B6
What happens at the far right and the far left ?
What is the end-behavior asymptote for f(x)=(x^2+4x-5)/(x-2) ?
There is an oblique asymptote at y=x+6 and a vertical asymptote at x=2. Is one of those the end-behavior asymptote?
3 answers
it approaches positive and negative infinity?
yes