Oblique Asymptotes :

Lines of the form y = mx + b, where m is the slope and b is any constant, such that f(x) approaches mx + b as x-> or x->-.

The following is an example of Oblique asymptote

Consider the following function. The graph has been plotted for the function f(x).

To find out the asymptote of the function f(x), we need to find the limit of the function f(x) for x tending to . Then, we find that 1/x -> 0, and x + (1/x) tends to increase and equals f(x). So, f(x) gets closer and closer to the line y = x.

When we find the limit of the function for x tending to - a similar explanation as the above applies. Also, when x-> 0 from the left, f(x)-> - and that as x-> 0 from the right, f(x)-> .

Also, the graph for the function has been drawn below :