show that the curve sqrt(x^2+4x) has two asymptotes: y=x+2 and y+-x-2.
Slant asymptotes are lines that the curve approaches as x --> +oo or x --> -oo. As x --> +oo or -oo, and the square root of this is . This is not a rigorous way of doing it. The mathematicians of MHF will pounce on this and make mince meat of it.
But I'm not sure you're at a level where a rigorous approach would make much sense, so you'll just have to make do with the one above.