The TI-92 graphing capability can help visualize the ideas involved in limits as x --> oo. You may want to look at the help module -- Graphing a function.
You can also investigate limits as x --> oo or as x --> -oo numerically as illustrated in the screen below. Notice that the TI-92 may sometimes give you exact rational numbers which for the present purposes are not as useful as decimal numbers. To get decimal numbers press green-diamond ENTER rather than just ENTER. For more on exact versus approximate answers click here.