If I'm reading what you have written correctly, you would like to find the asymptotes of

and

. An asymptote is simply a function that the graph approaches for increasing or decreasing values of x.

Mr F says: You are referring to a particular type of asymptote known as an oblique asymptote. Horizontal asymptotes are a special case of such asymptotes. There is another type of asymptote known as a vertical asymptote. These asymptotes are vertical lines passing through values of x that make the function undefined.
And in these cases, the important factor is that x is in the denominator. When you have x in the denominator, the constant part of the denominator becomes less important for increasing values of x. So for the first question, the asymptote is

and for the second question, the asymptote is

.

**Mr F says: NO! This is wrong.**
[snip]