I just can't wrap my head around this. I don't know if this is true I just came to conclusion with this

Question

if the limit of x--> +/-inf = L (if the limit of x going to pos/neg infinity gives you a number L) does that mean that L is a horizontal asymptote ?

if the limit of x---a = +/-inf (if the limit of x going to "a" gives you a +/- inf ) does that mean it's a vertical asymptote?

Answer 1

You are correct in both cases.

Consider f(x) = 1/x and f(x) = tan(x)